Sunday, July 31, 2011

Hijacking geekdom: geeks vs. freaks

The more cachet the term "geek" gains, the more distorted it becomes. We see this most recently in Ada Calhoun's piece in this weekend's New York Times Magazine Lives Column. Ms. Calhoun, now an accomplished writer and speaker, was the editor of the junior high school paper, attended parties and sleepovers, and had as her best friend the most popular boy at school, who once asked her out (she turned him down). Why, she asks, did she identify herself as an outcast?

The No. 1 suspect: late-1980s and early-’90s popular culture. In every book, movie or TV show, nerds were cool and the popular kids were lame. There was integrity to being an outsider. You didn’t want to be beautiful, popular Lea Thompson in “Some Kind of Wonderful”; you wanted to be the tomboy drummer Mary Stuart Masterson.
But how geeky were these pop culture cool kids anyway? The coolest protagonists of Freaks and Geeks, for example, weren't the geeks (the two younger male characters who were often played for laughs), but the freaks. And when has it ever not been cool to be a tomboy?

People forget that there are two types of outcast. There are those who are so socially awkward, and/or clueless, and/or narrowly intellectual that they have few or no friends who aren't equally geeky. And then there those who, often more deliberately, violate mainstream standards for gender, clothing, behavior, and extra curricular activities (eschewing leadership, football, and cheerleading).

When people depict geeks as cool, they're invariably depicting not the true geeks but the freaks. We see this most recently in Alexandra Robbins' Geeks will Inherit the World, which I blog about here, noting that:
The students she profiles are a “popular bitch,” a victim of racism, and a social under-achiever who is openly gay. They're certainly ostracized, at least by some, but not because they’re geeks.
Indeed, many people, if not those in the mainstream/majority, view freaks as cool, and they do so precisely because such kids deliberately flout mainstream standards.

The problem with twsting the term "geek" around to mean "freak" is that it's all too easy to pretend that geeks have it easier than they actually do, and that the rest of us don't need to make much more of an effort to appreciate them for who they really are.

Friday, July 29, 2011

Math problem of the week: 7th grade Connected vs. 6th grade Singapore Math

Fractions, percent, and ratio problems:

I. From the final Connections section of the 7th grade Connected Mathematics "Comparing and Scaling: Investigation 2, Comparing Ratios, Percents, and Fractions" [click to enlarge]:

II. From the first review in the 6th Grade Primary Mathematics 6A Workbook:

III. Extra Credit:

Suppose a news story reports that 100% of Amazon reviewers give only one star to a Connected Math book. The publisher think this means that 100% of the parents don't understand how math has changed in the 21st century. Do you agree with him or her? If not, what does the statement mean?

Wednesday, July 27, 2011

The anti-anti-Romantic child bias

More from Patricia Gilman's The Anti-Romantic Child:

Over and over again, I've found that even ostensibly supportive and sympathetic advocates for special-needs children subtly privilege some minds, some learning styles, some disabilities over others. In particular, in depreciating rote learning, esoteric obserssions, and memorization, they favor the dyslexic over the hyperlexic mind.
I'd never before thought of my right-brain vs. left-brain dichotomy, and the bias against left-brainers, in terms of dyslexia vs. hyperlexia, but Gilman's discussion rings true. She quotes dyslexia expert Sally Shaywitz describes dyslexia as "an island of weakness in a sea of strengths," associated "in many cases... with an ability to solve problems in original ways, to think not rotely but intuitively and holistically."

"In contrast to this," Gilman writes, "the implication in almost everything I'd read, from Web sites to academic articles, was that hyperlexia is an island of strength in a sea of weaknesses."

So, too, with "book smarts," "mere calculation" skills, "reductionist" science and engineering skills, and any other number of left-brain talents. All in all, not just islands, but an archipelago of Macronesian proportions.

Monday, July 25, 2011

Hyperlexia vs. autism

Priscilla Gillman's recently released book The Anti-Romantic Child raises anew for me the question of of autism subtypes. Here are some excerpts about Gilman's son Benj's development:

He recognized all the letters by about fourteen months (he loved to find the a, b, c, d on a J. Crew of Pottery Barn page), receited the alphabet with ease at sixteen months, read single words at twenty-two months, and began to read entire books fluently just after turning two...

Numbers were similarly fascinating to him. He could count from one to twenty by about fourteen months, and from one to one hundred shortly thereafter. He was able to tell time on our VCR counter by eighteen months. He learned hor to tell time digitally, and is we said "What time is it?" he would run up to the VCF, look at it, and proudly say, "Time is two fifteen," or "three thirty," or whatever. He would often grab started strangers' watches in the supermarket and greet visitors to our house with a friendly swipe at their watch.

...By studying [children's art books], Benj was able to recognize all shapes (not just tirangle, circle, square, but also hexagon, star, rhombus, and octagon) and colors (including orange, gray, and purple) at a little under two years old.

When he encountered a new person, he'd read the writing on their T-shirt, or call out the time on their watch, or find a letter of number in the shape of their jewelry... As a two year old, he wanted to spend most of his team reading, counting, or making long alphabet and number chains and spelling out words with his letter/number blocks. He'd cover the floor of our small apartment with these clocks, arranged in perfectly straight lines, with A or 1 at the front and Z or 20 at the end.

From about age two on, his obsession with letters and numbers dominated all of our outings...
And here is Benj, at around two and a half, visiting a preschool class:
He delightedly beat out the rhythm of the song they were singing and joined in perfectly on the chorus despite having never heard the song before... Everyone was watching him and he didn't notice at all.
The song ended and Benj--alone--clapped vigorously. Suddenly he strode forward purposefully toward the group. He walked right up to the group of kids, then pushed past a child on his way to... a huge hoop earring dangling from the ear of the teacher. Fasinated, he reached out to grab the earring and cried, "The letter O!"
This last episode is what spurs Gilman's worries. Re-examining his development, she realizes that:
Benj had never used gestures to express his desires and feelings: no waving, no pointing, no shaking his head no or nodding yes...
And, despite his on-target language development (single words just before one year; two-word phrases at two):
Most of Benj's spoken language was actually echolalia (repeating or echoing other people's language rather than creating spontaneous sentences).
With the echolalia comes pronoun reversal:
When he work up in the morning or from a nap and we went in to him, he'd say "Did you have a good sleep"? or "Are we getting up?" ... When he was done eating and/or wanted out of his high chair, he'd say "Are you done?" or "Do you want to get down?"
Googling phrases about early reading and trouble answering questions, Gilman soon find herself reading about a condition called hyperlexia, defined by the following core symptoms:
  • A precocious ability to read words, far above what would be expected at their chronological age or an intense fascination with letters or numbers
  • Significant difficulty understanding verbal language
  • Abnormal social skills, difficulty in socializing and interacting appropriately with people
Where, in all this, is autism? That Benj might be autistic, Gilman admits, is her deepest fear. And the Yale Child Study Center, evaluating Benj, allays it:
Benjamin did not "meet the diagnostic criteria for autistic spectrum disorder"--primarily because he was so "warm" and "related."
"Warmth" and "relatedness" do not appear in the official DSM-IV criteria for autism. Instead, we have (bold-faces are mine):
(A) qualitative impairment in social interaction, as manifested by at least two of the following:

1. marked impairments in the use of multiple nonverbal behaviors such as eye-to-eye gaze, facial expression, body posture, and gestures to regulate social interaction

2. failure to develop peer relationships appropriate to developmental level

3. a lack of spontaneous seeking to share enjoyment, interests, or achievements with other people, (e.g., by a lack of showing, bringing, or pointing out objects of interest to other people)

4. lack of social or emotional reciprocity ( note: in the description, it gives the following as examples: not actively participating in simple social play or games, preferring solitary activities, or involving others in activities only as tools or "mechanical" aids )
(B) qualitative impairments in communication as manifested by at least one of the following:

1. delay in, or total lack of, the development of spoken language (not accompanied by an attempt to compensate through alternative modes of communication such as gesture or mime)

2. in individuals with adequate speech, marked impairment in the ability to initiate or sustain a conversation with others

3. stereotyped and repetitive use of language or idiosyncratic language

4. lack of varied, spontaneous make-believe play or social imitative play appropriate to developmental level

(C) restricted repetitive and stereotyped patterns of behavior, interests and activities, as manifested by at least two of the following:

1. encompassing preoccupation with one or more stereotyped and restricted patterns of interest that is abnormal either in intensity or focus

2. apparently inflexible adherence to specific, nonfunctional routines or rituals

3. stereotyped and repetitive motor mannerisms (e.g hand or finger flapping or twisting, or complex whole-body movements)

4. persistent preoccupation with parts of objects

(II) Delays or abnormal functioning in at least one of the following areas, with onset prior to age 3 years:

(A) social interaction

(B) language as used in social communication

(C) symbolic or imaginative play
As for "hyperlexia," it is nowhere to be found--at least in the DSM-IV. In the forthcoming DSM-V, of course, the same will be true of "Asperger's Syndrome." Eventually, perhaps, this will dampen the fear and desperation that is typically inspired by the alternative diagnosis of autism.

Saturday, July 23, 2011

Reductionist critiques of science

In his otherwise fantastic book, The Ominovore's Dilemma  (on J's summer reading list for science), Michael Pollan has this to say about the "scientific" reduction of soil fertility to nitrogen, phosphorus, and potassium (N, P and K):

To reduce such a vast biological complexity to NPK represented the scientific method at its reductionist worst. Complex qualities are reduced to simple quantities; biology gives way to chemistry... When we mistake what we can know for all there is to know, a healthy appreciation of one’s ignorance in the face of a mystery like soil fertility gives way to the hubris that we can treat nature as a machine.
This "reductionist science," Pollan writes, "works by breaking such systems down into their component parts in order to understand how they work and then manipulating them — one variable at a time."

To be fair to Pollan, it's not clear whether he's using "reductionist" as a restrictive or nonrestrictive adjective. Is he talking about reductionist science (chemistry?) as opposed to non-reductionist science (biology?), or is he speaking of science in general, which is generally reductionist?

Whichever it is, Pollan contrasts it with the more mystical, holistic views of English agronomist Sir Albert Howard, who wanted farmers to mimic natural processes and "regard their farms less like machines than living organisms":
He’s telling us we don’t need to understand how humus works or what compost does in order to make good use of it. Our ignorance of the teeming wilderness that is soil (even the act of regarding it as a wilderness) is no impediment to nurturing it. To the contrary, a healthy sense of all we don’t know — even a sense of mystery — keeps us from reaching for oversimplifications and technological silver bullets.
Pollan thus recaps the tired dichotomies our right-brained culture is so fond of: reductionist (bad) vs. holistic (good); mechanistic (bad) vs. naturalistic (good); breaking things down and manipulating them (bad) vs. reveling in mystery (good). But however many more variables it has than N, K, and P, and however elaborately they interconnect, nature is still a machine. True, we don't have to understand how it works to make use of it, but breaking nature down and manipulating its parts systematically (i.e., one variable at a time) can actually make us more appreciative of if its emergent mysteries, and less likely to oversimplify things, as we gain insight into just how intricate and intricately balanced it all is.

Pollan critiques "our fetishism of science as the only credible tool with which to approach nature." Does he honestly think that most Americans view nature in terms of science? That would presume a level of basic scientific understanding that most of us, increasingly, lack. But as a tool for understanding nature, what could be better than science?  Indeed, as Pollan himself grudgingly notes a few pages later, it is scientific inquiry, not mystical thinking, that has ultimately found support for Sir Howard's claims:
As it happens, in the years since Howard wrote, science has provided support for a great many of his unscientific claims: Plants grown in synthetically fertilized soils are less nourishing than ones grown in composted soils; such plants are more vulnerable to diseases and insect pests; polycultures are more productive and less prone to disease than monocultures; and that in fact the health of the soil, plant, animal, human, and even nation are, as Howard claimed, connected along lines we can now begin to draw with empirical confidence.
As it happens. Yes, nature is complicated. So is scientific inquiry--biology and chemistry alike. Let's not oversimplify either.

Thursday, July 21, 2011

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

I. A 4th grade Investigations (TERC) assignment, assigned at the end of September [click to enlarge]:

II. From a similar point in the 4th grade Singapore Math Primary Mathematics 4A Workbook (p. 30) [click to enlarge]:

III. Extra Credit

Which is more mathematically engaging: "naming" numbers, or simplifying the "number names" provided to you by your educators?

Tuesday, July 19, 2011

David Sedaris on language lessons

Ah, grammar. How dry. How boring. Right up there with those tedious times tables and those soul-sapping algorithms of arithmetic.

But then here's David Sedaris in the latest New Yorker reflecting on the Pimsleur language program:

Thanks to Japanese I and II, I’m able to buy train tickets, count to nine hundred and ninety-nine thousand, and say, whenever someone is giving me change, “Now you are giving me change.” I can manage in a restaurant, take a cab, and even make small talk with the driver. “Do you have children?” I ask. “Will you take a vacation this year?” “Where to?” When he turns it around, as Japanese cabdrivers are inclined to do, I tell him that I have three children, a big boy and two little girls. If Pimsleur included “I am a middle-aged homosexual and thus make do with a niece I never see and a very small godson,” I’d say that. In the meantime, I work with what I have.
The problem is that Pimsleur is all about mimicry:
Pimsleur's a big help when it comes to pronunciation. The actors are native speakers, and they don't slow down for your benefit. The drawbacks are that they never explain anything or teach you to think for yourself. Instead of being provided with building-blocks which would allow you to construct a sentence of your own, you're left using the hundreds or thousands of sentences you have memorized. That means waiting for a particular situation to arise in order to comment on it; either that or becoming one of those weird non-sequitur people, the kind who, when asked a question about paint color, answer, "There is a bank in front of the train station,"or, "Mrs. Yamada Ito has been playing tennis for fifteen years."
What are those "building-blocks which would allow you to construct a sentence of your own," and, equally importantly, the rules that tell you how to put those building blocks together? That dry, tedious, soul-sapping entity known (or sort of known) as Grammar.

However tedious and soul-sapping it is to do so, mastering a language's grammar rules is the only way to move beyond mimicry and use the language creatively: the only way to move from  "I have three children, a big boy and two little girls" to “I am a middle-aged homosexual and thus make do with a niece I never see and a very small godson.”

Pimsleur isn't alone in presuming that you can master a language without learning its grammar; the biggest seller of this fiction is Rosetta Stone (whose slogan, ironically, is "More than Words. Understanding.") Other grammar-denialists (as I discuss here) are k12 foreign language curriculum developers, as well as (as I discuss here) autism therapists and the general American public. It's a vicious cycle that worsens with each succeeding generation of mis-educated students, more of whom need to spend time attempting to converse with Japanese cabbies before foisting their language lessons on the rest of us. Thank you, David Sedaris, for yours!

Sunday, July 17, 2011

Screening for social skills in med school admissions

Like everyone, I've heard plenty of stories of doctors who egregiously lack bedside manner, and I've certainly had my share of face-to-face encounters with them. But I'm nonetheless troubled by what may be a new trend in medical admissions policies, reported on by last Monday's New York Times:

Doctors save lives, but they can sometimes be insufferable know-it-alls who bully nurses and do not listen to patients. Medical schools have traditionally done little to screen out such flawed applicants or to train them to behave better, but that is changing.
At Virginia Tech Carilion, the nation’s newest medical school, administrators decided against relying solely on grades, test scores and hourlong interviews to determine who got in. Instead, the school invited candidates to the admissions equivalent of speed-dating: nine brief interviews that forced candidates to show they had the social skills to navigate a health care system in which good communication has become critical....
The first thing I thought of when I read this were all the Aspie people I know who can't help being insufferable know-it-alls with poor listening skills but who nonetheless but might make excellent contributions to medical research. How would they fare during the Virginia Tech application process?
At Virginia Tech Carilion, 26 candidates showed up on a Saturday in March and stood with their backs to the doors of 26 small rooms. When a bell sounded, the applicants spun around and read a sheet of paper taped to the door that described an ethical conundrum. Two minutes later, the bell sounded again and the applicants charged into the small rooms and found an interviewer waiting. A chorus of cheerful greetings rang out, and the doors shut. The candidates had eight minutes to discuss that room’s situation. Then they moved to the next room, the next surprise conundrum and the next interviewer, who scored each applicant with a number and sometimes a brief note. 
“We are trying to weed out the students who look great on paper but haven’t developed the people or communication skills we think are important,” said Dr. Stephen Workman, associate dean for admissions and administration at Virginia Tech Carilion.
Nor is Virginia Tech the only school seeking to screen applicants based on social skills: 
Dr. Charles Prober, senior associate dean at the Stanford University School of Medicine, said Stanford always valued social skills in students — particularly the ability to work collaboratively with colleagues and establish trust with patients — but did not have a reliable way of ferreting these skills out until adopting mini interviews.
Med schools seem to be forgetting that not all MDs work with nurses and patients--or in environments where teamwork skills are essential:
Administrators at Virginia Tech Carilion say teamwork has become so essential to medicine that the school not only chooses its students based on their willingness and ability to collaborate effectively, but also requires students to take teamwork classes.
Thus, for Virginia Tech anyway, passing the social skills tests is a rigid requirement for admission:
“Our school intends to graduate physicians who can communicate with patients and work in a team,” said Dr. Cynda Ann Johnson, the dean of the Virginia Tech Carilion School of Medicine, which opened in August 2010. “So if people do poorly on the M.M.I. [the above-described "multiple mini interview"], they will not be offered positions in our class.”
Wouldn't it make more sense to use screening tools like the M.M.I. later on in the process, and only for those specializations that actually require people skills?

Friday, July 15, 2011

Math problems of the week: 5th grade

5th grade applied math problems: the 1920's vs. the 21st Century (click on pictures to enlarge):

I. The second-to-last "Everyday Use of Numbers" problem set in Hamilton's Essentials of Arithmetic, First Book (published in 1919), p. 363:

II. The second-to-last applied math problem set in the 5th grade Everyday Mathematics Student Math Journal Volume 2, p. 428:
III. Extra Credit

1. Which problem set is more "everyday"?

2. Which problem set is better suited to the everyday realities of classroom mangement?

Wednesday, July 13, 2011

Everything but the curriculum, II

Additional places where the word "curriculum" is conspicuously absent:

Education Reform's Two-Month Warning

Reforming the Refomers

Tuesday, July 12, 2011

Reflecting on real problems, real research, and real solutions

My friend Meg Campbell, the founder and executive director of the Codman Academy Charter Public School in Dorchester Massachusetts, has written a thoughtful piece for the Huffington Post on teachers reflecting and working together on practical problems--in this case, the issue of grade inflation. What's particularly refreshing about this piece is how it shows educators opening their minds to new research findings and considering that research carefully.  Too often, schools don't allow teachers, let alone research, a role in decision making, deferring instead to bureaucrats or to out-of-touch education professors.

(Meg, by the way, also teaches at the Harvard Graduate School of Education, and so she belongs to that rarer bread of in-touch education professor).

Meg's careful consideration of practical problems reminds me very much of Joanne Jacobs' account of a charter school in San Jose California (Our School).

Sunday, July 10, 2011

Left-brain strategies for improving student behavior

There's been a lot of news lately about the steps to which schools are going to reduce bullying and improve student behavior. Typically these programs involve some sort of specific anti-bullying programs, or social-emotional curricula, that either take students away from academics and/or having them spend more time working in groups.

I've already argued that having students work in groups, far from reducing bullying, creates further opportunities for it. Beyond this, it seems to me that a more promising way to reduce bullying and improve behavior isn't to further dilute academics with non-academic activities, but to drastically reduce the time that children are academically disengaged.

In my book I argue that, when people look for causes of misbehavior, they too often search for social and emotional causes, overlooking one other major contributor: boredom. But consider the arenas in which children are most likely to misbehave: long lines; long car trips; waiting rooms; long-winded discussions. In the classroom, when are children most likely to fidget, space out, bother each other, or otherwise act up? During the science experiment, or while waiting for the experiment to begin? While taking a timed multiplication test, or while waiting for their slower group mates to understand the group assignment? While reading about the Barbarian invasions, or during a circle time discussion about how we all need to be nice to each other? 

In their book The Learning Gap one of the greatest contrasts between American classrooms and their East Asian counterparts that authors Stevenson and Stigler discover is in how much time we Americans waste--whether in transitions between classes, in transitions between activities, or in transitions from subtask to subtask. As every parent knows, transitions can bring out the absolute worst in children. 

To instead bring out the best, let's focus on making school relentlessly interesting. For Constructivists and sociability-obsessed right-brainers, this means one thing. But for the rest of us, most children included, it means cognitively challenging material for each student at his or her level, the best sorts of creativity and relevance, and a drastic reduction in time students spend disengaged and/or waiting--whether in line, in unsupervised group activities, during long-winded discussions, or throughout all those inefficient hands-on activities that so dominate the Constructivist paradigm.

Friday, July 8, 2011

Math problems of the week: 2nd grade Everyday Math vs. French Math

A. The final multiplication word problems in the Everyday Math grade 2 Student Math Journal:

1. 3 vans full of people. How many people in all?

[picture of a van] vans people per van people in all
Holds 10 people ________ ___________ __________

Answer: ___ people
Number model: ___ X ___ = ____

2. 4 insects on the flower. How many legs in all?

[picture of a ladybug] insects legs per insect legs in all
Has 6 legs ________ __________ _________
Answer: ___ legs
Number model: ___ X ___ = ____

3. 9 windows, How many panes in all?

[picture of a window] windows panes per window panes in all
Has 4 panes ________ ___________ _________

Answer: ___ panes
Number model: ___ X ___ = ____

B. The sample grade 2 (CE 1) multiplication word problems from Professeur Phifix, a web resource for French curriculum materials (translated from the French):

For each problem, write down the calculation and a sentence as your answer.

Mr. Doudou wants to buy three armchairs for his vacation home. He decides not to spend more than 300 Euros. He goes to a store and finds armchairs at 35 euros each. He goes to another store and sees some for 28 euros, but these ones he doesn't like as much.

Can he buy the chairs from the first store, or must he buy those from the second store?

A person wants to take a 7 day trip to Greece. He goes to a travel agency which proposes to him a trip at 68 euros a day. The plane trip lasts 3 hours.

What is the total cost of this trip?

A school puts on a show to raise money for a computer. Tickets cost 6 euros. 234 people attend the show.

How much money was raised?

III. Extra Credit:
Can differences between French and American culture explain why American students are doing single digit multiplication and filling out forms while their French counterparts are doing multi-digit multiplication and working things out on their own?
[Another problem I've recycled from earlier, inspired by recent arguments made in defense of Reform Math that invoke culture and politics. People need need to remember that it's not just the Singaporeans (and the East Asians), but also the French (and the Europeans), who use a significantly more challenging, and more traditional, math curriculum].

Wednesday, July 6, 2011

Measuring higher level scientific thinking?

(A take-home quiz given recently to my 8th grade son).

I'm tempted to add a question or two:

11. Suppose questions 1 through 10 above represent an attempt to assess the ability to assess experimental design. Which of the following should be done to improve this assessment:

a. Omitting obvious experimental design errors that no one is likely to make, especially when they are displayed clearly in pictures (different sized circles) or spelled out explicitly in words ("in the sun;" "in the shade").

b. Avoiding vaguenesses ("some bacteria"? "milk"?) that make it hard to understand what the experiment includes and does not include (more than one kind of bacteria? of milk?).

c. Not confusing concepts with simple key word mappings ("control"="measurable variable"; "constant"="same amount").

d. Field-testing this exam to find out whether it makes any predictions about students' experiment design skills.

e. All of the above, and more (can experimental design skills be abstracted away from content, or, like so many other instances of "higher level thinking," are they domain-specific?)

Monday, July 4, 2011

Blaming children for their ignorance, IV: the role of teachers

Perhaps most steadfast in blaming children and their families, rather than K12 instruction, for children's ignorance, are K12 teachers. Here's what one high school math teacher commented on one of Joanne Jacobs's recent posts on math education:
In most cases, it’s not because they were poorly taught, but because they didn’t
have the cognitive ability to learn the subject properly.
Her evidence?
High school and middle school math teachers have to pass fairly rigorous
competency tests, and have for years.
To which one commenter replied:
Ah, but not elementary school math teachers. They get minimal training in math. As for their mathematical aptitudes, what I witnessed when I audited a math methods class at a highly reputed education school was a majority of students who were extremely weak in math. Many, for example, confessed to getting help from their fathers, husbands, and boy friends on the weekly problems (which were at about the level of 4th-6th grade Singapore Math).

It is essential to remember that it’s in elementary school the problems begin! This is true even at the most advantaged schools. Take, for example, the joint collaboration with the above ed school and the lcoal school district. The existence of this school has caused real estate prices in its catchment area nearly to double. Because it’s perceived as a great place to teach (among other perks, class size is capped well below the city-wide class size limits), many teachers apply. And the school has site selection privileges, so its principal can hand-pick the teachers. So you'd think that every elementary school teacher who gets a job at this school would have a good grasp of math.

You would be wrong.  Some teachers have been hired after confessing during their interviews (which parents can attend) that they hate math and aren’t good at it.
The school has also picked a terrible math curriculum (Investigations in Number, Data, and Space).
As a result, only those children who are getting outside tutoring in math are mastering the fundamentals of arithmetic that are prerequisites for succeeding in algebra.
Given how terrible things are at the elementary level even in some of our better schools, how can we even begin to know what the mathematical capacities are of those children who don’t have access to outside tutoring? No child should be taught math by anyone who says they hate math and/or aren't good at it. No child taught by such a teacher should be labeled as "lacking the cognitive ability to learn the subject properly."

That said, there are still plenty of mathematically capable teachers out there. Given how any resistance to the curriculum by teachers counts as potentially job-terminating "insubordination," how much can we blame teachers for the low performance of those students who don't have access to outside tutoring?

Indeed, given how terrible the Reform Math (and other Constructivist) curricula are, how can we even begin to know what the teaching skills are of those teachers who don't have access to alternative curricula?

If we're looking for who's responsible for students' ignorance, we should start with those who create, fund, promote, and mandate the various incarnations of Reform Math and other Constructivist curricula (Balanced Literacy, anyone?), along with those responsible for the dumbed-down, No Child Left Behind tests that keep all this securely in place.

Saturday, July 2, 2011

multiple solutions, group work, hands-on discovery learning, learning styles, and reversing home and school

Besides creativity, personal connections, verbalizing answers, and self-esteem, there are several other problematic areas within today's K12 instruction that I think can still be put to good use.

Multiple solutions
While requiring students to solve easy arithmetic problems in multiple ways, as Reform Math routinely does, is tedious and pointless, there can be a virtue to solving harder, multi-step problems in more than one way--not least because this is often the best way to check your answers.

Showing your work
Again, this depends on how hard the problems are. With hard, multi-step problems there is often work to show even for those who can perform complicated calculations in their heads, and teachers sometimes can't gauge whether students know what they're doing in such cases unless they examine this work.

Group discussions
While working in small groups in classrooms has all sorts of downsides (distractions and inefficiencies, confusion, unequal conctributions, opportunities for bullying, etc.) these can be avoided when the whole class functions as a group, led, of course, by the teacher. Class-level group discussions are perhaps the best venues for brainstorming solutions to problems and sharing observations during literary analysis.

Hands-on, discovery learning

Used in moderation and planned out carefully, hands-on learning can be an efficient way to learn certain things and remember them later--especially when it comes to science experiments. I once devised a hands-on activity for a 10th grade geometry in which students manipulate angles to discover that the angles of a triangle sum to 180 degrees.

Of course, none of these general ideas are new, and anyone who thinks that long-ago classrooms never applied them is laboring under the dry, dill & kill caricature of traditional schools promulgated by Constructivist alcolytes via the fallacy of the false dilemma.