Saturday, December 31, 2011

Anonymous and Chemprof on Yet another front in the war against math…entrepreneurs


Anonymous said...

I find it odd that he chose Geometry to eliminate when it has so many practical applications. Couldn't you use knowledge of geometry, history, a foreign language or a bunch of other things as the basis of a successful business?

I'm a small business owner. I never took a course in entrepreneurship but I figured out how to create a business plan pretty easily. Millions of entrepreneurs figured out how to fill unmet needs without ever taking a high school course in how to do it. High schools usually offer business and finance classes that pretty much cover the financial stuff. They offer writing classes which cover how to write. And colleges offer Marketing courses.
All you need to learn to become an entrepreneur is already being offered at the high school or college level. An entrepreneurship course is completely unnecessary.

ChemProf said...

I think part of this push is a (poor) response to college for all. High schools no longer offer business or finance courses, because those aren't college prep, so now there is a push to move those courses into the college prep curriculum.

C_T on the Pitfalls and plusses of multiple choice tests


C T said...

Sometimes in college, I was lucky enough to have courses with great multiple choice exams. Not only did I feel like they were fairly assessing me, but I learned while taking the tests and felt stretched intellectually. That some tests are written poorly is no reason to demonize them as some people do; just write better ones.

Anonymous, Amanda, and Deidre Mundy on Autism and visual thinking


Anonymous said...

This is a very astute observation. People on the autistic spectrum do need extra prompts to capture and focus their attention (as do ADHD and ADD people). Providing a visual prompt that they can access constantly or repeatedly and on their own is a great help, and would explain why nonverbal children with autism are rarely taught sign language, which is visual but evanescent.

Amanda said...

Another hypothesis: good diagrams and other visuals can make underlying structure and linkages much clearer than a page of text or a teacher explanation on their own: maybe what seems to work with autistic children would actually be good for all children.

Deirdre Mundy said...

With respect to lists, organization methods, visual schedules, etc---

In my experience, the difference isn't that these things DON'T help normal people as well--it's that the ADHD kids need more overt instruction, practice and time with the organizational tools that seem to be second nature to the "normal" kids. The same goes for phonics, I think-- the kids I've seen who are "natural readers" also use phonics, they just picked them up without overt instruction.....

Friday, December 30, 2011

Anonymous on Who is Christopher Columbus?


Anonymous said...

In our fair city, Christopher Columbus Day is not even celebrated (school's in session), apparently because he is seen as part of the "history of oppression." My children never learned about him in school and they learned about the Mayflower from library books (outside of school time).
Back in 2007, a note was sent to teachers about Thanksgiving saying: Fact: For many Indian people, 'Thanksgiving' is a time of mourning ... a bitter reminder of 500 years of betrayal returned for friendship.

Deirdre Mundy, Laura, and momof4 on Differentiated instruction in the one room school house

Deirdre Mundy said...

The other plus of the one-room school house was that grade-acceleration was easy and subject-based. If a first grader was a math whiz, he could just work on the third grade lesson and recite math with them, even if he needed to stay with his age mates for reading.

On the other hand, discipline was probably LESS of a problem since the majority of families who bothered to send their kids to school would punish them if they were disobeying the teacher......

I think the closest modern equivalent to the one room school house may be home schooling-- which is more possible now, since in Laura's day simply providing food and clothing for the household was a full time job for BOTH pioneer parents and their kids!

Also, the pioneer school day was shorter and had a long recess... but the school wasn't expected to provide social services, just education....

And (to be negative here) pioneer one-room schools weren't the norm--- in the East, there was enough population density to support larger schools and individual grades. (Compare Laura's experience in Minnesota to Betsy and Tacy's, only about 80 miles down the road and 20 years later! )

And pioneers were a self-selecting bunch, in terms of hard work and discipline-- school was more likely to be a treat than a punishment, whereas for the city kids the alternative to school wasn't working the farm, but wandering around buying candy and playing with the hordes of other kids.......

So I'm not sure we really could recapture the ideal...
Laura said...

I've done some work on my family history - and many of my relatives attended one room schoolhouses, or small schools. A couple were even school teachers. It is simply amazing to read their letters and diaries. Their level of knowledge, even if they only attended school to 6th grade or 8th grade, was more than our High School graduates today! (Not counting current events of course!).

My great-grandmother spoke only Swedish until she went to school, and only went until 8th grade. However, she could easily hold her own in any Community College today.

On the other hand, my daughter suffered through current educational practices for a few years, when she attended a local parochial school. It wasn't as bad as the local public schools, but they used a lot of group work, journaling and other constructivist methods.

So to answer your question - Yes, I would join you going back to the "Good, Ol' Days" of Schooling. In a heart-beat!

momof4 said...

My DH attended a Catholic ES where all the teachers were nuns and had been trained by their order. It sounds like the Normal Schools some of my ES teachers attended. In both cases, teacher preparation was both explicit and practical; no fuzzy theories, just math, phonics, grammar and the disciplines. Today, the teachers at Catholic schools have attended the same ed schools as the public teachers, so it's not surprising to see the same stuff in the parochial classrooms.

I also have relatives who had less than a HS education and who were far better-educated than today's HS grads (or better). I also had relatives who attended one-room schools until HS, and acceleration was common.

Deirdre; I loved the Betsy-Tacy books - haven't heard anyone else even mention them!

Anonymous and Laura on Special Education and Everyday Math, revisited


Anonymous said...

I don't think the ones that could do this, i.e. modify teaching methods, include good material, teach to the students, rather than to the book, are permitted to do so by administrators that buy into a curriculum and require "fidelity" of instruction in that curriculum. Only.

Laura said...

When my daughter's school changed its math curriculum from a traditional one to a more constructivist one (Not as bad as Everyday Math - but bad enough) - school became a real struggle. It became the straw that broke this Mama's back. I couldn't explain the math to her, because I didn't "Get it!" 4th grade math... *sigh*

We ended pulling her out and homeschooling her and using Saxon Math. So much better. Night and Day difference. This year we switched to Abeka Math for other reasons (It is still very traditional and straight-forward - but keeps on one subject longer than Saxon).
I just cannot understand how "they" expect any children (especially autistic children) to learn any kind of math, from this load of garbage they have heaped upon the educational system. Unbelievable.

Thursday, December 29, 2011

Niels Henrik Abel on 1900s math vs. Interactive Math Program

Niels Henrik Abel said...

"Homework 1: Past Experiences:
"Include this so you can look back later and compare your experiences before this year to your experiences with the Interactive Mathematics Program."
(Student response)

Well, let's see. Last year I had geometry with Mr. Smith. He was a tough teacher, but I'm really glad I had him, because we actually learned how to do some proofs, which he said we'd need to know, especially if we want to take calculus and physics and understand all that stuff. I was psyched, because I had read about Newton and Leibnitz and Kepler, and I really wanted to learn about this magical calculus that allowed them to understand some of the mysteries of nature. I was supposed to take intermediate algebra and trig this year, but they changed the math program and I got stuck with this stupid "Interactive Mathematics" thing. There's hardly any math at all, and what little there is is not going to help me at all when I finally do manage to get to calculus and physics. Give me back my math, please, instead of this crap.

Niels Henrik Abel and ChemProf on Please visit an actual classroom before you make recommendations, VII


Niels Henrik Abel said...

I really don't get the inordinate fascination with "quantitative literacy." If you want to get a handle on finance, exponential growth/decay, and all the other "real world" crap that they stick in these types of textbooks, you still need to have a solid foundation of algebra, and the mathematical reasoning that goes along with it.
Can't get away from all those nasty, "irrelevant" Xs and Ys after all. And what Deirdre said is true: the "real world," "relevant" math is harder and more obtuse than the straightforward, "contrived" problems.

ChemProf said...

I teach freshman chemistry, and can tell you that students find algebra with lots of different symbols much more difficult than algebra with x. In kinetics, one of the most dreaded topics is finding a rate law from a mechanism, since it is pure symbolic manipulation.
It is also odd that they include "how computers are programs" when it is almost impossible to find a real programming class in high schools. I'm quite curious about what they think this would look like -- I'm betting it would be a lot of messing with the GUI and not much programming.

Deirdre Mundy on Accelerating within grade level with new new new Math


Deirdre Mundy said...

The other thing is that while "going deeper" might be entertaining for geomerty or precal or calc when the kids get older and can have fun with proofs and whatnot, there's not much place to go with elementary math.
If the class is calculating areas and volumes, well, sure, you can give the brighter kids irregular shapes and have them try to figure out the areas---but once they've mastered the technique for that, where do they go?
If the class is working on multi-digit addition, and the kid's mastered it, what are you going to do? Just tack on more digits? In many cases, going "deeper" instead of accelerating just means soul-crushing busy work and more practice with the same algorithms the kids have already mastered.
On the other hand, it's easier for a teacher to just give MORE work than it is for her to give harder work, especially if she's not particularly math-inclined herself.

The funny thing is, at least when I was in school, the teachers claimed that making us help the slow kids helped teach us 'compassion.'
As a fifth grader, I didn't have the maturity to learn 'compassion' from that. I just resented them for their slowness and ended up doing the work FOR them so that I could get back to reading whatever decent book I'd hidden in my desk.

All that it taught me was snobbery. We would have been better off with a lecture on how different people are better at different things, and that sure, I could do school well, but Suzy Slowpoke could embroider and I couldn't even sew a button without impaling myself. And then the teachers could have HELPED SS THEMSELVES instead of having another little kid do it! (who admittedly, was sort of socially retarded, so maybe if I'd been a normal 10 year old I would have been better, but looking back, I was more like a 6 or 7 year old on the whole 'dealing with others' thing)

Anyway, the other problem is that for a lot of the smarter kids, they CAN'T help the slower kids, because they literally can't understand how someone could fail to grasp something so intuitive. I mean, how many pictures do you have to draw to get someone to realize that 1/2=2/4=3/6=7/14 etc. etc. As a ten year old, all you want to do is scream and impale your head on a spike so the stupidity of it all will stop making your brain hurt.

As an adult, dealing with the same sort of things, I realized that some people just take a LOT more time and repetition to grasp things than others do... but as a kid, you really do assume that everyone's brain works like yours and that if they can't remember something it's because they're deliberately forgetting it.
Maybe instead of "going deeper," they should just make all the advanced kids work on motor skills.... it would probably be more helpful in the long run.....

Wednesday, December 28, 2011

Deirdre Mundy on autism diaries XXVII: roundup of the latest experimentation and mischief


Deirdre Mundy said...

My dad apparently had great luck with "frogs and salamanders in the ice cubes" as a boy. But his pranks were aimed at making sisters scream, not parents groan.

…spring peepers are very small, so they fit in well. As are some salamanders. And for the others, if you, say, freeze them and put them in the container used for finished cubes, and your sister grabs a handfull and dumps them into her coke w/o looking, and then the salamanders thaw and wake up....
Well, apparently it's legendary. I have NOT let my kids do this, because I LIKE the frogs and salamanders and don't want them to get hurt or scared. :)

But more seriously, if your kid likes electronics, understands electronics and is GOOD at electronics, you should totally encourage him! Maybe you can redirect some of the 'prank' into "useful?" Like hit thrift stores, pick up non-functioning devices, and challenge him to fix them?

Brian Rude on Measuring higher-level scientific thinking


Brian Rude said...

Arguing against the scientific method is sort of like arguing against motherhood and apple pie. But I'm used to being the grinch, so here goes.
I would argue that in general the type of science appropriate for elementary and secondary education is primarily descriptive. To be scientifically literate students must build up a mass of information. That takes years to do. Without a solid foundation of information, much of which can be called descriptive information, there is nothing on which critical thinking can be applied.
We do not know about the world primarily through experimentation. We learn about the world primarily by making plausibility estimates. Contrived experimentation is important, but only key points in the development of a science. Contrived experimentation is a very ineffective and inefficient for learning science. Explanation and plausibility fitting are effective and efficient.

I have developed ideas along these lines in two articles on my website. "Rules and Methods of Science" is at, and "The Rationale Of Laboratory Exercises In The Teaching Of Science" is at

LexAequitas on Will geeks inherit the earth?

LexAequitas said...

I have 2 sons (actually 3, but for this explanation only the older two are needed).

Son one is bright, highly analytical, has a good grasp on logic and math, has a rock-solid memory, is tremendously interested in science and is straightforward and honest and opinionated. He has sometimes rocky relationships with peers due to his honesty and shyness. Similarly, in conferences his teachers dismiss his intelligence as almost an afterthought, and focus most of their attention on whether he's giving them the proper amount of respect/writing neatly/organizing his desk/doing things on their schedule. His grades tend to be highly uneven.

Son 2 (3 years younger) is of about average intellect, has a tenuous grasp of logic, and a poor memory -- but is also friendly, extremely outgoing, and usually cheerful. He makes friends easily, has enough sense not to go against the teacher, and even his rebelliousness/mischievousness is often viewed by teachers with a smile and wink. His great talent is to get everyone to love him.
I can't necessarily say that son 2 will do well in life and son 1 won't. But so far, son 2 is having a far easier time and enjoying his life a lot more.

Tuesday, December 27, 2011

Brian Rude, kcab and ChemProf on The virtues of explaining your answers


Brian Rude said...

I think it was in about fifth grade when one day the teacher told us, "If you can't say it, you don't know it." That always stayed with me, not because I believed it, but because I questioned it. I wondered if it were really true. It's totally understandable that a teacher would say that, but that doesn't mean it's really true. Over my lifetime I have given the idea some thought and concluded that it's not a simple matter. There are times when explicitly and precisely verbalizing what we are learning is very important. There are other times when verbalizing what we are learning is practically impossible and certainly not worth the time trying. Language is obviously a very powerful tool that we ought to develop as much as we can. But it is definitely not true that thought is only linguistic. With a little reflection one can come up with plenty of examples of nonverbal thought.

I have a few years experience teaching college math. Many times a student would come to my office for help. A common pattern was repeated many times. After getting oriented to the students difficulty (not always a quick or easy task) and selecting an appropriate problem to work on, I would be struggling to find just the right words to explain something, when the student would suddenly say, "Oh, I get it!". That would be my cue to shut up. Language is a wonderful tool, but a lot of thought consists of assembling ideas together in certain ways. When helping students I use language identify the mathematical ideas needed and assemble them in a way that will apply to the problem at hand. But the actual assembling of ideas itself is not linguistic so much as conceptual.
Most of us are quite adept at using a computer word processing program for writing. That involves a lot of learning. Were we forced to verbalize each step along the way when we learned? Can you verbalize everything you know about writing with a computer? Would it be beneficial to try to verbalize all that? What about driving. Have you ever tried to verbalize everything you know about driving? Would that be beneficial?
All this is not to say that language is not important. Obviously it is. But you can over do a good thing. I have been aware of the "explain your answer" fad in math education, but have always considered it just that, a fad. In a math class I think "explain your answer" should be translated into "show your work". And writing in a math class should simply mean "show your work".

kcab said...

I think the very best math students are able to explain their answers as well as work the problems. In reading a couple of books recently, "Count Down" and "Perfect Rigor", it seemed to me that the systems described for developing top math contest competitors had a lot of emphasis on teaching kids (not necessarily neurotypical) to explain their thought processes. My own mathy child is extremely good at explaining work, particularly aloud to others (the process of writing it seems tedious to him at times).

I think there is something to the idea that being able to explain one's work requires understanding a problem in a different way. I wonder though, whether anything is lost in the translation to words - is it necessary sometimes to hold off on the verbalization for a bit so that the problem can be completely seen? Wasn't there something about verbal descriptions of a memory altering and weakening the memory itself? I wonder if other non-verbal information is similarly affected.

ChemProf said...

In General Chemistry, I teach basic quantum mechanics. I occasionally get a very verbal student who wants me to explain why atoms act the way they do at a more fundamental level. But at that fundamental level, you are really talking about mathematics (or a description of mathematics -- saying "a superposition of basis sets" to a student who is in Calc I is not too meaningful). A few have been insistent that I must be able to explain in words, since "if you can't say it, you don't know it," and I've had to shut them down with a little bra-ket notation! So, there are a few things that aren't easily explained in words. And the people I know who really internalize quantum (I am not one of them) seem to do so in some non-verbal way.

Barry Garelick, Anonymous, and Amy P on The harmful effects of uttering “think” and “know”


Barry Garelick said...

I remember being puzzled by what "thinking" was and asked my mother "how do you think?" when I was in first grade. In first grade, we had a reading/writing activity book called "The Think and Do Book" so my conception of thinking was that it was different than "doing". But in time, I began to understand. I do not believe I suffered ill effects from exposure to such term.

Anonymous said...

Most people don't need to "think like a mathematician." That is a bizarre idea. Just as most children who are learning a sport (rules, skills, physical conditioning, and so forth) do not need to learn the physiological processes behind muscle function. Why would you postpone learning the sport until the kids are old enough to understand molecular biology? And, learning the sport by example and practice doesn't prevent the children from (later) learning why the muscles work the way they do. Now, it's true that children do need to think "big picutre" about the sport they are learning; and they need to bring an analytical approach to that learning. But that is not the same as understanding the "why" before attacking the "how."

Amy P said...

In language, there are a lot of forms that are pretty weird if you stop and think about them. For instance, if I say, "There is a cookie in the jar," what does "There" mean? Why not just say, "A cookie is in the jar." Likewise, when we say "It is cold today," what does "It" mean? Why not just say, "Is cold today." We use this stuff without thinking about it, without registering that it's peculiar.

Mnemosyne's Notebook on Honors classes for all


Mnemosyne's Notebook said...

The Swiftian Solution would be to offer only AP Courses, since those would be richest in content.

Here in Hawaii, we teachers are taught that putting gifted students together with the less able is good for both. The research papers we were given to read during out teacher certification classes all showed that the less capable students did better on their projects when paired with more capable students(!). When I asked for results showing that the gifted students did better when paired with the less capable (as opposed to be paired with other gifted students) I was given anecdotes, but no data of real comparisons.

So, AP classes for all, with one gifted student per group - and only project work. That'll learn 'em all.

Monday, December 26, 2011

Kcab and ChemProf on Math problem of the week: 1900s algebra vs. Connected Mathematics


 kcab said...

I'm struck by how much more fun the problems in Wentworth are than those in Connected Math. Also, they remind me of math contest problems, which my kids find enjoyable.

ChemProf said...

I guarantee that some of my incoming students, who do reasonably well in calculus or pre-calc, would be stumped by these problems. One issue I see a lot in chemistry is the inability to take a word problem and figure out the math embedded within it. I'd love to see students spend more time on "inauthentic" problems like these in middle school and high school.

Happy Elf Mom, Deirdre Mundy and Niels Henrik Abel on Models for Autism: the math skills tradeoff


Happy Elf Mom said...

Not sure. I know that Emperor is gifted in maths and NOT gifted in social skills. I keep him home to educate him because I'm pretty sure they're not going to teach my third grader algebra. :)

But when he goes to school someday, I'm afraid they will eat him alive. He just has no clue how to carry on a conversation and doesn't understand why people don't like him. I'm very sad for him in that aspect of his life.

Deirdre Mundy said...

The big problem I see is that schools have taken over 'socialization' as well as education. It used to be that kids were 'socialized' by family, the neighborhood, the church, the after school job.
Now school is responsible, and so everything has to become about academics AND socialization.
Teachers don't see the problem because ES teachers seem to be drawn from the segment of society who pick up social skills easily and naturally. So they see "more success!" because kids who would have struggle with academics are now excelling (because they're also graded on social skills.)

On the other hand, for the kids who struggle with social skills (Autism spectrum, ADHD, just plain quirky), passing as 'normal' takes a PHENOMENAL amount of effort. And even if they work really hard, they STILL come off as defective, just less defective than previously. (Speaking from personal experience here! ;) )

So, if they're forced to focus on appearing 'normal,' they STILL fail on social skills, but they also have no effort to spare to actually concentrate on the material!

I see this all the time with my ADHD daughter (runs in our family!! ;) )
If I make her sit still and display 'typical attentive student' body language, that's ALL she can do (until she melts down from exhaustion and stress and worry and failure.)
If I let her be....odd... she can master the material quickly, enjoys academics, and draws connections, thinks, and wonders.
Then we save the HARD stuff (personal space, ettiquitte, not crying, standing mostly still) for other times of day and other activities (CCD, art class, tai kwo do, speech therapy, church, playdates, grocery stores.)
But Math is math. Reading is reading. History is history.

But the schools insist on joining social skills with EVERYTHING, and then can't understand why the kids who stink at "social' get depressed and give up.
Even though a kid who dislikes MATH gets all sorts of sympathy and encouragement.
But, of course, social skills are easy and fun!....if you're normal and the ES teachers.....

Anonymous said...

I''m not remotely on the autistic spectrum, but I am someone who likes to choose when to be "social" and when not to. A classroom where I was expected to learn through interaction with other students, even if they were focused and on-task at all times, even if we were all at the same level, even if this were not an inefficient way to learn (usually), that classroom would have been a nightmare for me. I actually enjoyed being a baby boomer who never experienced a K-8 classroom with fewer than 35 kids in it; with those numbers, you do whole-class instruction and the students ask the teacher questions if they don't understand. Teachers facilitate whole-class discussions. The interactions I saw going on between the children working in groups in my own children's classrooms was not a model for good learning, and was painful to one of my (also not autistic) son, irritating to one daughter, and a matter of indifference to the other.

Niels Henrik Abel said...

Even though a kid who dislikes MATH gets all sorts of sympathy and encouragement.
But, of course, social skills are easy and fun!....if you're normal and the ES teachers.....
So true, so true!! Not being adept at math or science is considered acceptable (at least tacitly so), but those who are introverted and prefer to study or play alone (or with a buddy or two, as opposed to a larger group) are marked as defective and needing treatment to cure them of their "anti-social" (if anything, "asocial" is more accurate) behavior.
I was always turned off by that narrow-minded, petty view towards "loners." When will people realize that there is a difference between "being alone" and "being lonely"?

Jen on Blaming children for their ignorance, II


Jen said...

Children aren't little adults.

The adults making curriculum seem to forget that a lot. They create things that would keep *their* attention about a subject they already understand.
I think this is why we get so much group thinking and "exploration" and the like before the students have just been taught. Directly. But direct teaching and practice seems boring for an adult who already understands it.

Sunday, December 25, 2011

RMD on Blaming Children for their Ignorance

RMD said...

I find it amazing that mankind has spent thousands of years trying to make sense of the world in a systematic way that helps us do really cool things, and modern pedagogy is willing to just let our kids experiment with the world assuming we don't have a 6000 year head start on our ancestors, rather than catching them up on the last 6000 years and then letting them experiment.

gasstationwithoutpumps and Deidre Mundy on Ideas that buzz: modern educators, clinicians, and writers


gasstationwithoutpumps said...

"Buzz" and faddism have a lot to do with funding of science and are almost the sole determinant of who succeeds as an artist.
In both fields it is difficult sometimes to distinguish the brilliant from the cranks and so the mediocre rule.

Deirdre Mundy said...

I think you'll find that many home-schoolers are also buzz-less education reformers-- we can't change the system, or even find a listening ear.... but we can at least fix the system for OUR OWN KIDS.

In my fantasy education reform, we'd replace 'academic' pre-k and K with "montessori for all."

It's not that montessori doesn't TEACH academics.. it just teaches them in an age appropriate manner. It also teaches habits of concentration and calm that many kids today seem to lack.

The thing that I find odd is that, in the US today, Montessori is basically the preserve of wealthy elites, even though it was originally developed for poor tenement children in Italy.

Anyway--homeschoolers actually, as a group, devote a fair amount of time to education and curriculum research. But, as parents, they mostly care about what works.
But when you're a stay-at-home, crunchy-granola-religious-pseudo-hippy, you don't generate buzz---it's more like ANTI-buzz.

Jerrid Kruse, Hainish, FedupMom, Barry Garelick, and LynnG on Between the basic elements and the fuzzy abstractions


Jerrid Kruse said...

My first reaction was that you haven't defined structure well enough so it ends up being this abstract concept - like the ones you lament. Then, I figured out what you mean by structure and your post makes much sense. (Examples are great, but are not a definition, sometimes the abstract is a very very good thing).
However, this structure you long for is most often reduced to a set of rules to be memorized rather than a set of understandings. Because the structure is interpreted this way, it rarely leads to the big ideas you are talking about. But hey, I was just glad to see you care about the big ideas.

Hainish said...

I don't think it's that teachers forget or want to forget structure, I think that it's below the radar for them. It doesn't even register. Instead of seeing the structure, they see the "lower-level" things--the names and dates and individual words--so they write it off as being too trivial to care about.

But, maybe I'm being uncharitable.

FedUpMom said...

At my younger daughter's school, they use Trailblazers math.

They've had a lot of complaints, of course, so in response they make the kids do a lot of very low level stuff -- computerized drill of adding and subtracting whole numbers, stuff like that.
The problem is that there's a whole layer of conceptual stuff that they still don't cover.
So they've got the airy-fairy "what's your favorite number?" level covered, and the bog-level drills covered, but none of the necessary concepts in between.

Barry Garelick said...

However, this structure you long for is most often reduced to a set of rules to be memorized rather than a set of understandings.
You don't teach a "set of understandings". The understandings are first about the procedures--presented in proper context, the understandings will follow. Sometimes the conceptual underpinnings will occur in a later grade/course. It wasn't until I took algebra, for example, that I understood why the invert and multiply rule for fractional division worked. In the meantime, however, I certainly knew when to apply fractional division to solve problems.

The hang-up over "big picture" is a continual confusion between epistemology and pedagogy. Novices don't learn to become experts by being given problems that only experts can solve.

Sweller talks about this in his article "Why Minimal Guidance During Instruction Doesn't Work":
According to Kyle (1980), scientific inquiry is a systematic and investigative performance ability incorporating unrestrained thinking capabilities after a person has acquired a broad, critical knowledge of the particular subject matter through formal teaching processes. It may not be equated with investigative methods of science teaching, self-instructional teaching techniques, or open-ended teaching techniques. Educators who confuse the two are guilty of the improper use of inquiry as a paradigm on which to base an instructional strategy.

LynnG said...

The cumulative building of knowledge in the various disciplines (and they are called "disciplines" for a reason) is under-appreciated in k-12 education.

In an effort to make everything relevant right now, the structure of knowledge has been lost.

I asked a couple 9th graders "which came first, the Vietnam War or the Civil War?" they had no idea. But they could all reflect at length about the evils of slavery and discrimination, without reference to any of the major events in the history of civil rights.
Our children have been taught that their feelings about big issues is far more important than knowledge of the these things.

Saturday, December 24, 2011

FedupMom, GasstationWithoutPumps, Anonymous on The Race to Remediation


FedUpMom said...

Katharine, I often hear people ask, "which is it -- are kids overworked or underprepared?"
I think it's a false dichotomy. It is absolutely possible for kids to be both overworked and underprepared, and I think it's extremely common.

How can this be? It's because the mountains of homework and test prep that our kids labor under are in fact meaningless crap.

Anonymous said...

Katherine, the high rejection rates of the top colleges (and many that are not top) is a direct result of the fact that today's students are likely to apply to 10 colleges rather than 3 (or even 1, which was common when I was in high school).

gasstationwithoutpumps said...

The pools have gotten bigger, but not better at the top schools. In fact, the increasing size of the application pools has resulted in dilution of the pools with more less-prepared students. As a result, criteria that worked well enough in the past at getting a decent entering class may fail on the weaker pool. (At one time random selection from the pool would have gotten a decent entering class, but not so much any more.)

Also, in most schools faculty don't select the entering class—admissions officers do. The admissions officers and the faculty may have very different ideas about what the ideal entering class is like. Admissions officers are much more interested in demographics (race, gender, geographic origin, … ) than in individual readiness, which may compromise their ability to select students who will do well in college.

Anonymous said...

At the same time, and in many of the same schools, some kids are underprepared and some kids are overachievers - both academically and in extracurriculars. A couple of years ago, a graduate wrote a book about the tremendous pressure on kids from her old HS; I'm very familiar with that school and there are plenty of relaxed kids (probably most) and some drifters. The overachievers do apply to many schools,often a mix of Ivies, the Duke type, UVA and UNC (as out-of-staters) and perhaps their state flagship school or a smaller private as their safe school. The issue of admissions people and academics having different priorities is also valid. I've often thought I'd like to see academic departments select their students with as much diligence and care as the coaches select their players. I'm sure it would be a different mix; the physics and math departments aren't likely to worry about one B in English from a math genius, but I know one kid that was rejected from MIT while they admitted a weaker math but better all-around kid from his school (same sex and race).

Deirdre Mundy on Models for Autism


Deirdre Mundy said...

Have you seen the trailers for Wretches and Jabberers? The men featured in that movie seem to be type 1.
Also, in terms of gluten and dairy avoidance 'curing' autism -- severe food allergies can cause autism-like symptoms in a child, BUT if avoiding the allergen 'cures' her, then it wasn't AUTISM. It was a food allergy. I think this is where a lot of the 'diet cure' advocates run into issues.

The doctor tells them that diet doesn't cure autism. They see a cure for their child. So look! Doctors are wrong! Actually, the Dr. is just commenting that the cure means it WASN'T autism in the first place....
The biggest issue I see with "the spectrum" is that it seems like we're taking a bunch of symptoms and saying "everyone with these symptoms must have the same underlying disorder!" When really, if I have a runny nose, it could be allergies, it could be a cold, it could be flu, it could be that I ate a bowl of curry, it could be that I stuck a foreign object up there.

Treating all runny noses as if they had the same cause would be insane.... but it seems like that's where we are with autism right now....

Lsquared, Deirdre Mundy, and Chemprof on More fallacies in the media about cooperative groups


Lsquared said...

I agree. My reference points are mostly math. Andrew Wiles proved Fermat's Last Theorem. He couldn't have done it if Ken Ribet hadn't proved that if the Taniyama-Shimura conjecture was proved, then it would also prove Fermat's last theorem, so it wasn't a result that was done without knowing other people's work, but when he was working on it, he worked completely alone, and didn't talk to anyone about what he was doing until he believed he had the solution. Science needs both the sharing of knowledge, and the persistence of the individual working alone. Collaborators aren't rare, but they aren't the only way to go, either.

Deirdre Mundy said...

Also, it seems to me that the most productive TRULY cooperative efforts in science have come from a partnership, or perhaps a trio. And these fruitful collaborations usually grow organically, out of a mutual interest, rather tahn being imposed from above.
So we get the Curies, and Watson,Crick and Franklin (and notice Franklin always gets left out.) and Miller-Urey, etc. etc....
So partnerships, not groups. And freely chosen ones. Totally UNLIKE what happens in a classroom environt when a teacher decides that "Groupwork is necessary for learning!!!"
Also, as an aside, in an elementary classroom, brainstorming is usually an exercise in stupid. Coming up with 20 lame ideas is NOT a good substitute for one or two GOOD ones.....
ChemProf said...

Since grad school, I've published many collaborative papers. Never did we sit and brainstorm. Sometimes we'd talk and argue a point, but often it was more iterative -- one person would write a draft, and the other person would read and comment on it, pointing out questions or problems with interpretation. It never resembled elementary-school "group work." In fact, I've found in general that the least productive meetings are the ones without some kind of first pass on paper or an agenda. Without that focus, even educated adults tend to just talk around the issue and waste time. Anyone who has ever sat through a faculty meeting without an agenda should be familiar with this phenomena.

Friday, December 23, 2011

Deirdre Mundy on eliminating busy work


But if you eliminated all the busy work, the school day would only be about an hour and a half long! And then people would have to PAY for babysitters!

Seriously -- My daughter's homeschooled day is about 1.5 hours long. But I don't count the time she spends coloring, drawing, making up stories, learning myths, doing wordfinds or watching documentaries as "school." School is the part of the day where she is doing the work that I've determined is necessary for her academic growth. (At this point, mostly reading and math). The other stuff is what she chooses to do for fun. I'm not going to give her 'credit' for drawing a diorama of African animals. BUT if she was in school, it would be a 'project.' And, honestly, it would probably have had all the joy sucked out of it.

Schools need busy work, because there is no way that a 6 year old can do PRODUCTIVE work for nearly 7 hours a day. And babysitting 25 kids at once means trying to keep them as quiet and sedentary as possible.

In my ideal world, the school day would stay under 3 hours long until 4th or 5th grade. But it would never fly. Somehow, we've grown to equate "time in a classroom" with "instruction time" and believe that "more" is the same as "More efficient."

Linda on the Pennsylvania State Assessment Anchors (PSSA)


Linda said...

Yes, the PSSA is taken in the spring of fourth grade. I teach at a school in PA that does Singapore and the PSSAs are the bane of my existence. There is practically no computation on the PSSAs and the kids are allowed to use calculators on most of it. Our students can do some really fantastic math, on which they are not tested. Basically, the month before the PSSAs we have to put the real math away and drill the kids in things like symmetry (there are a million questions on symmetry) and other random bits of unimportant stuff that they love to focus on. The higher up the kids get the farther back in Singapore I have to dig for test review. The PSSA fourth grade picture graphs are in the Singapore book 2B.

Barry Garelick, FMA, and JC on The Stereotype of Rote Learning in East Asian Classrooms:


Barry Garelick said...

The argument posited by the Times and others is compelling for reform math apologists of all stripes and colors. By saying that the Chinese system is test oriented, then getting high marks on a test is evidence of lower order thinking, and that getting low marks on a test is evidence of higher order thinking. Sort of like the excuse I used to use when a beagle I had wouldn't obey any of my commands. I told people it was because she was so smart she knew exactly what the command was but she just was choosing not to follow it.

FMA said...

Saying that Asians are less creative or that tests like PISA aren't a good indicator of competence are self-comforting mechanisms. We see that they are ahead of us but we want to comfort ourselves by saying it doesn't mean anthing because (enter excuse here).
America really needs another Sputnik Moment. Obviously PISA results aren't waking us up to reality. Maybe China trouncing us on clean energy will wake us up. They're already ahead of us. Hopefully we will wake up before it's too late to catch up.
Bob Compton, producer of 2 Million Minutes and the upcoming film The Finland Phenomenon put it well:

"If your kid has graduated three years behind the rest of the world in every subject, how do they catch up? It’s very serious."

JC said...

Why so much opposition to drilling in American education? Neuroscientists say that something has been learned when a connection for it has been created in the brain. Building these connections requires repetition (drilling). You simply can't learn without repetition. The brain simply doesn't build connections without it.

Creativity won't be much use to our students if they don't know anything. Knowledge and creativity have to go hand-in-hand to be useful.

FMA said...

"Why so much opposition to drilling in American education? Neuroscientists say that something has been learned when a connection for it has been created in the brain. Building these connections requires repetition (drilling)."

There is a big disconnect between how we actually learn and how too many educators think we should learn. It is a problem of ideology over evidence.

Favorite comments of 2011!

You taught me; you moved me; you made me laugh--it was such a pleasure, and an education, to reread your comments of 2011. I've collected my favorite ones of many, and there are so many of them that I'll be posting 3 sets a day for approximately the next ten days. Enjoy!

Wednesday, December 21, 2011

Might suspending your preconceptions and biases be something to strive for?

This week's Education Week is promoting not just "creativity," but "personal connections" and "relevance." In "Can Readers Really Stay Within the Standards Lines?", authors Maja Wilson, a former high school English teacher and current teacher of literacy instruction at the University of Maine, and Thomas Newkirk, a professor of English at the University of New Hampshire, express concern about the common core standards for K12 English.

What specifically concerns them is what the common core standards (CCS) say that K12 readers should be focusing on--namely "the text itself," or "the text on its own terms." They find this an old- fashioned ("early and mid-1900s") notion, and also disagree with CCS's idea that "while the personal connections and judgments of the reader may enter in later, they should do so only after students demonstrate 'a clear understanding of what they read.'" Nor do they like CCS's proposal that publishers should pose "text-dependent questions [that] can only be answered by careful scrutiny of the text" and that "80 to 90 percent of the Reading Standards in each grade require text-dependent analysis; accordingly, aligned curriculum materials should have a similar percentage of text-dependent questions." Finally, they question CCS's conception of what close readings are all about: "Student knowledge drawn from the text is demonstrated when the student uses evidence from the text to support a claim about the text."

All this, they write, both represses the reader, and shows "distrust of reader response." Second, "this readerly repression is unnatural, and probably impossible":

Since you are obviously still reading this Commentary, you be the judge. Have you stayed within "the text itself"? Have you cordoned off preconceptions, biases, prior reading, and associations until you finish and comprehend this text?
Third, if you don't make things relevant to students' lives, how can they possibly find them interesting:
All the instruction in the world won't help a reader who has already decided that a text is distant and irrelevant. But helping students understand the text itself means helping students find themselves in it. We worry that if textbooks, curriculum, and assessments align themselves to the view of reading in the common-core guidelines, students will become alienated from the very complex texts with which they will be required to grapple.
Wilson and Newkirk then contrast two ways one would teach, say, Nicholas Carr's 2008 essay from The Atlantic, "Is Google Making Us Stupid?" Their way:
Before assigning the essay, we would have students log their media use for a day (texts, emails, video games, TV, reading, surfing the Internet) and share this 24-hour profile with classmates. We might ask students to free-write and perhaps debate the question: "What advantages or disadvantages do you see in this pattern of media use?" This "gateway" activity would prepare students to think about Carr's argument. As they read, they'd be mentally comparing their own position with Carr's. Surely, we want them to understand Carr's argument, but we'd help them do that by making use of their experiences and opinions.
In the classroom envisioned by the standards guidelines, these personal connections and opinions might be allowed later, after students have encountered and come to know Carr's text "on its own terms." Some preteaching would be allowed in the common-core classroom—as long as it didn't distract from the text. So students might be presented with a list of vocabulary words in the article or maybe be given information about the genre being read. But as they read, their attention would be focused almost exclusively on Carr's argument.
I agree with Wilson and Newkirk that it's difficult for readers to "cordon off preconceptions and biases." But does that make it desirable to encourage the opposite? I realize I'm about to suggest something as old-fashioned as the common core standards, but here goes: Might preconceptions and biases be things that potentially interfere with accurate text comprehension; things, in other words, that we might want K12 schools to discourage? Maybe my impressions are distorted by my own preconceptions and biases, but it seems to me that, when my students write analyses of the week's reading, the main way in which they go wrong (when they go wrong) is by focusing insufficiently on the text, and one of the main reasons why their focus is insufficient is because they are... distracted by their preconceptions and biases.

In fact, you see this everywhere--particularly in areas where conflicting, strongly-held beliefs come into play. How often have you posted a careful, meticulously qualified comment on the Internet, only to have someone who disagrees with you mischaracterize your "some" as "all," your "not all" as "none," your "sometimes" as "always," or your "not always" as "never;" exaggerate your evaluative phrases; erase your qualifications and delineations; or otherwise obliterate all the subtlety you've tried so hard to communicate, distorting your position into a straw man to be zealously ripped apart? While this tactic may simply indicate that your adversary doesn't have any good arguments against your actual views, it's often also a case in point of preconceptions and biases interfering with reading comprehension.

I suspect that that's what's going in a recent Amazon customer review of my book. Here Jennifer Bardsley, who has also appeared on this blog and who describes herself as holding views on educational theory that are "the polar opposite" of mine, writes:
Despite what Dr. Beals claims, STEM careers require communication and collaboration. Do engineers create digital cameras in isolation? Do cancer researches conduct private experiments and then keep mum about their findings? In my opinion, gently encouraging students to become better about sharing their ideas and thinking can only help them in the long run.*
But here's a passage straight from the book (Raising a Left-Brain Child in a Right Brain World):
There's an important difference, people forget, between cooperation and collaboration. Yes, many modern mathematical and scientific puzzles are large enough that multiple scholars attack them simultaneously. But they do so not by divvying up the pieces, working independently, and only reconvening to present and tweak one another's solutions. They collaborate, but they mostly work separately, not cooperatively. (p. 42; italics as in the book).
(There's also an entire section devoted to "Teaching Rules for Conversations," which includes strategies for encouraging unsocial children to share their thoughts more effectively with others.)

Perhaps if we did more to encourage people to begin by suspending their biases and immersing themselves in other people's arguments--or worlds, or whatever else their words create--we'd have a society that is not only more literate, but also more open-mined and tolerant. For this, the common core standards for K12 English may be a start--so long as they don't end up being distorted by people's preconceptions and biases.
*Ms Bardsley also faults Left Brain Child for lacking footnotes and a bibliography, not noting that references are repeatedly embedded in the text (publishers' preferred format for trade books), or that some of the world's most heavily footnoted texts are complete nonsense.

Monday, December 19, 2011

Online learning revisited: death knell for the lecture

Perhaps the best reason for claiming that the lectures are dead, or inappropriate for 21st century classrooms, is that online learning modes offer better alternatives. This is the case made by Daphne Koller, a professor in the Stanford Artificial Intelligence Laboratory who teaches one of Stanford's three online computer science classes, and who is also the author of a recent Science Times article entitled Death Knell for the Lecture: Technology as a Passport to Personalized Education.

Since I recently wrote a blog post critiquing online learning environments, I was particularly interested in what Koller had to say. One of her best arguments is about the flexibility of videotaped presentations, which can be much shorter than lectures:

Presenting content in short, bite-size chunks, rather than monolithic hourlong lectures, is better suited to students’ attention spans, and provides the flexibility to tailor instruction to individual students. Those with less preparation can dwell longer on background material without feeling uncomfortable about how they might be perceived by classmates or the instructor.

Conversely, students with an aptitude for the topic can move ahead rapidly, avoiding boredom and disengagement. In short, everyone has access to a personalized experience that resembles individual tutoring.
The only concern I have about this is that it leaves it up to the students to decide when they're ready to skip things or move on. They--particularly the weaker, less motivated among them--may not always be the best judges of this, and may be tempted to skip over content that they don't find interesting (which may specifically include stuff they don't understand).

While software programs can't ensure that students are devoting sufficient attention to the video presentations, they can control their access to the specific assignments, providing additional tasks when students show weaknesses and advancing them to the next level if and only if they've mastered the current one. Ideally these two features--student control over which presentations to which, and ability-based advancement--allow, as Koller points out, a kind of individualized tutoring that may optimize learning. In this connection, Koller notes that:
In 1984, Benjamin Bloom showed that individual tutoring had a huge advantage over standard lecture environments: The average tutored student performed better than 98 percent of the students in the standard class.
Third, as Koller points out, while online curricula may not be able to address all areas of difficulty or confusion, the broader online environment allows efficient ways to pool student questions and to connect those with questions to those with answers:
Our Stanford courses provide a forum in which students can vote on questions and answers, allowing the most important questions to be answered quickly — often by another student. In the future, we can adapt Web technology to support even more interactive formats, like real-time group discussions, affordably and at large scale.
Furthermore, as others have noted as well, putting teaching presentations online allows for:
the flipped classroom, [where] teachers have time to interact with students, motivate them and challenge them.
Fourth, online environments are a better laboratory than brick and mortar schools are for identifying what works in education:
More broadly, the online format gives us the ability to identify what works. Until now, many education studies have been based on populations of a few dozen students. Online technology can capture every click: what students watched more than once, where they paused, what mistakes they made. This mass of data is an invaluable resource for understanding the learning process and figuring out which strategies really serve students best.
All these things, indeed, are the big advantages of online learning. Beyond this, the more instruction you automate, the more money you save and the more you can circumvent shortages of qualified teachers. But there's one big limitation to automated instruction. As I know from evaluating language teaching software programs and creating such programs myself, it's quite easy to automate a passive, multiple choice, right-or-wrong answer learning protocol. But a truly active learning environment--one in which students receive helpful feedback about where they went wrong and what to do about it--is both more more pedagogically effective, and much more difficult to automate. Here, Koller may be overly optimistic
For many types of questions, we now have methods to automatically assess students’ work, allowing them to practice while receiving instant feedback about their performance. With some effort in technology development, our ability to check answers for many types of questions will get closer and closer to that of human graders.
It's telling that the online subject with which Koller is most familiar is computer science. As I note in my earlier post:
The only truly active learning environment that I've ever seen in any software program for any academic subject is that which a computer programming language platform provides for--what else?--computer programming. Only here does the feedback--the error messages or the unexpected outputs--precisely reflect what you've done wrong.
We're a long way from achieving that in any other subject (with the exception of English morphsyntax for English language learners).

Saturday, December 17, 2011

More distorting openers from Edweek

First we have, from last week's issue, the headline: "To Boost Learning, Start With Emotional Health." The implication: that dealing with emotional health takes precedence over academics.

By the middle of the article, however, this position has mutated into something more moderate:

But evidence has shown that when it comes to the success of our children, both [health and education] are equally important.
As for specific proposals, quoting author Jane Isaacs Lowe, a senior program officer at the Robert Wood Johnson Foundation, these are:
Playworks, which supports a full-time, trained staff person—often an AmeriCorps member—to facilitate recess in schools in low-income communities... [to] help kids play new and classic games, teach them to resolve conflicts safely, and encourage healthy physical activity at recess and throughout the school day.
Achool-based health centers [in partnership with] the Center for Health and Health Care in Schools, or CHHCS, another nonprofit organization, to address both physical- and mental-health issues.
Both of these sound eminently reasonable; why embed them in standard-issue right-brained propaganda?

Then, in this week's issue, we have "Studies Explore How to Nurture Students' Creativity" and its opening paragraph:
In the continuing debate about American competitiveness in the global economy, politicians and educators alike have pointed not to students' test scores, but to their creativity and ingenuity, as models for the rest of the world.
And, a couple of paragraphs later:
Howard E. Gardner, a professor of cognition and education at Harvard University, considers creativity one of five "minds," or ways of thinking—along with discipline, synthesis, respect, and ethics—that will be essential for young people to succeed in the future.
"While cognitive capacities are obviously valuable for creating," he said, "only those of a robust, risk-taking personality and temperament are likely to pursue a creative path."
As in Edweek's earlier STEAM article, the assumption here is that the arts are the best way to inspire creativity. Only if you proceed beyond the first section of the article do you discover that (in what could have been the article's title) Studies Show We Don't Know How to Use the Arts to Inspire Creativity:
Ellen Winner, the psychology chair and the director of the Arts and Mind Lab at Boston College, told participants at the Learning and the Brain conference that in a continuing series of studies on arts education and creativity, she had found "very little evidence that studying the arts improves grades or test scores, or that studying the arts improves creativity.

"These transfer claims have been posited without any particular mechanism; there's a lot of magical thinking going on," said Ms. Winner.
And only if you continue reading do you learn how problematic it is when teachers attempt to assess creativity:
Even educators hoping to improve students' creativity can inadvertently quash their willingness to take creative risks, according to Robert J. Sternberg, an expert in intelligence-testing research, who is provost and senior vice president of Oklahoma State University in Stillwater.

"Risk is essential to creativity, … but if you want to get into the good college and the good graduate school and the good job, you don't want to take too big a risk," Mr. Sternberg said at the National Academy of Education meeting. "Schools often encourage you to do the opposite of what you'd need to be creative."

In one study, for example, Mr. Sternberg found that university students in New Haven who took more risks got higher marks for creativity in a drawing contest, but for a writing contest, "when the kids in essays took controversial stands, the raters often rated them down," he said.
For all this, the article concludes on an optimistic note. First, cites unnamed "experts" as claiming that:
Schools can help students become more generally creative, going beyond simply mastering content knowledge or how to perform specific skills to using their imagination to solve problems.
Then, with paragraph on Ellen Winner that contradicts the earlier one, it reasserta s the notion that arts classes can inspire creativity:
In her most recent research, Ms. Winner and her colleagues spent a year interviewing teachers and videotaping five arts classes at Boston Arts Academy and the Walnut Hill School for the Arts in Natick, Mass. From that material, the researchers identified eight "habits of mind" taught as part of art class that transfer to other subjects.

Among those habits was one called "stretching and exploration"—the equivalent of creativity in the context of the study.

The "stretch and explore" habit in art class looks similar to experimentation in science classes. Rather than simply telling a student how to perform a task, Ms. Winner said, the teacher might ask students "to try new things, take risks, and not be afraid of mistakes, but instead to capitalize on their mistakes."
Only if you scrutinize the next paragraph does it become clear that this approach, like so many other fashionable approaches in education today, is as yet unsupported by evidence:
Now, Ms. Winner and her colleagues are involved in a two-year longitudinal study to develop measures to gauge whether the "stretching and exploring" that students learn to do in art class transfers to more creative thinking and problem-solving in math or science class.
Think we'll hear back from Edweek when the definitive results come in? If so, how exactly will Edweek sandwich them, and can we predict the headline ahead of time?

Tuesday, December 13, 2011

Artsy science: what about sciency art, IV

An article in this week's Education Week entitled  "Building STEAM: Blending the Arts With STEM Subjects couldn't help but grab my attention. Here's the opener:

The acronym STEM—shorthand for science, technology, engineering, and mathematics—has quickly taken hold in education policy circles, but some experts in the arts community and beyond suggest it may be missing another initial to make the combination more powerful. The idea? Move from STEM to STEAM, with an A for the arts.
The actual term "STEAM," author Erik Robelin admits, may not catch on; but there are buzzwords aplenty to buttress it:
...momentum appears to be mounting to explore ways that the intersection of the arts with the STEM fields can enhance student engagement and learning, and even help unlock creative thinking and innovation.
One core idea ...STEAM advocates emphasize is that the arts hold great potential to foster creativity and new ways of thinking that can help unleash STEM innovation.
“There is creativity in STEM itself, super genius in it, ... but in arts education, it really is the raison d’etre to be out of the box, to accept the chaos,” said John Maeda, the president of the Rhode Island School of Design, in Providence.
Artists and designers, he said, are “risk takers, they can think around corners.”
Carrie Fitzsimmons, the executive director of ArtScience Labs, the Cambridge, Mass.-based organization that manages the ArtScience Prize. “It’s all fun, experiential learning, but we’re teaching them to be critical thinkers and problem-solvers.”
Naturally, Robelin doesn't interview any actual scientists on whether boosting scientific creativity and student engagement in science depends on the arts.  He does reference, however:
a 2008 study led by Robert Root-Bernstein of Michigan State University, which found that Nobel laureates in the sciences were 22 times more likely than scientists in general to be involved in the performing arts.
And, he adds:
Albert Einstein was an accomplished violinist. And then there’s the Renaissance figure who some view as the personification of STEAM: Leonardo da Vinci, the Italian painter and sculptor who also made a name for himself as a scientist, engineer, and inventor.
Specific examples of STEAM include the following:
Through art-making projects, students at one [Philadelphia] school manipulated the abstract concepts underlying fractions for a more concrete understanding of how they work. The students even created a “fraction mural” displayed at the school.

...performing artists in theater, music, dance, and puppetry working alongside classroom teachers in preschool and kindergarten settings.

[A team of students] creating public art installations that communicate how people around the world struggle to gain access to fresh water.

...watercolor paintings of cells...."beautiful artistic renderings, and students could pick out the structures that they had been studying."
A number of highly enthusiastic non-scientists are quoted, including Karen Childress-Evans, the San Diego school district’s director of visual and performing arts; Jenny Montgomery, an art teacher at the Dayton Regional STEM School (quoted above in reference to the watercolors); Harvey Seifter, an expert in arts-based learning; and U.S. Rep. James Langevin (D. Rhode Island), who:
introduced a House resolution to highlight how “the innovative practices of art and design play an essential role in improving STEM education and advancing STEM research.” 
Less enthusiastic are the scientists, whose comments are buried in the dead center of the article: Alan J. Friedman, a former head of the New York Hall of Science, who holds a doctorate in physics, and Susan Singer, a Carleton College biology professor. Says Friedman:
"They [art and science] also have some very essential differences that are at the core of what they are, which is why I have trouble with STEAM.”
The scientists may also be more troubled than the non-scientists are by the lack of STEAM-supporting data:
“There is no question, to me, the critical missing piece is the data,” said Mr. Seifter. He adds that even as he’s witnessed the power of the intersection, he sees a critical need for a “solid body of empirical knowledge about what the arts bring to the STEM equation.”

Indeed, research examining the effect of arts integration on student achievement across disciplines appears to show mixed results.
But there are plenty of funds for the fishing expeditions that will secure for the Powers that Be the data they know must be out there:
The NSF has provided research grants and underwritten a number of conferences and workshops around the nation this year.
One advocate of the STEM to STEAM push is Harvey Seifter, the director of the Art of Science Learning, a project financed by an NSF grant that organized three conferences last spring in Washington, Chicago, and San Diego that brought together scientists, artists, and researchers, as well as educators, business leaders, and policymakers to explore how the arts can be engaged to strengthen STEM learning and skills and produce a more creative American workforce.
The Philadelphia Arts in Education Partnership, with support from a $1.1 million Education Department grant, is working with city schools to help elementary students better understand abstract concepts in science and mathematics, such as fractions and geometric shapes, through art-making projects.
In California, a $1.1 million grant last year by the state’s Postsecondary Education Commission, using federal teacher-quality aid, is supporting the 134,000-student San Diego school district’s work linking the arts with science in grades 3-5.
The data is surely just around the corner, even if it's mostly not about academic achievement. For example, the Philadelphia Arts in Education Partnership has a four-year grant from the Education Department’s Arts in Education Model Development and Dissemination program which includes:
an “intense research component” and will look at a variety of effects, including student test scores, suspensions, and unexcused absences, as well as parent engagement in homework and changes in teaching practices.
Even some of the non-scientists, however, have their reservations about STEAM.  Here, again, is Karen Childress-Evans:
“It’s not just teaching science through the arts, but teaching science and the arts together, and what comes from that is more than either of them standing alone.”
And here, again, is Jenny Montgomery:
At the same time, Ms. Montgomery said, even in a STEM school, it’s important for art not simply to be valued for its application to other disciplines.

“I also uphold the value of making art for art’s sake,” she said, “that students have an opportunity just to engage in art for the sheer joy of it.”
And science for science's sake? Or using science in art class? None of these folks seem to notice, or care, that the latter is nonexistent, and that the former has been receding from our classrooms for years now. Perhaps if the Erik Robelen had interviewed a few more scientists, and not buried their words in the dead center of his article, this issue would have surfaced. But if you once again follow the money, taking a look at the article's acknowledgements, you see why it doesn't:
Coverage of leadership, expanded learning time, and arts education is supported in part by a grant from The Wallace Foundation.
Is there no Power that Be out there interested funding coverage of, and research on science for science's sake?

Sunday, December 11, 2011

Why open-ended projects aren't so open-ended after all

The other day, as my daughter and I biked home from her violin lesson, we found a large truck blocking our usual way. So we tried continuing straight instead of turning right, which led us to the far end of the park, which we then realized we could cut through on one of its diagonal paths. This turned out to be a much nicer, and even slightly faster, way home. Without the obstacle, we might never have deviated from our routine to discover it.

Jonah Lehrer makes a similar point in his Head Case column in a recent weekend edition of the Wall Street Journal. He proposes that the reason why most artistic genres are highly constrained is that they force artists to come up with new ideas. Rhyming constraints, for example, can force poets to find words they might otherwise never have thought of using in the context at hand. Unexpected word choices transport poetry from the trite and well trodden, bringing us fresh associations and imagery.

Lehrer's piece references a couple of recent experiments. Unfortunately, as far as I can tell, these don't really bolster his case: they seem to be more about distractions than about obstacles. I predict, however, that experiments that do measure the effects of obstacles on creativity will eventually prove him right.

If he is, then we have one more argument against open-ended assignments. Not only do they not provide enough structure to help autistic spectrum children and other left-brainers get started; they also may not sufficiently jostle students in general out of their habits and inspire them to seek out roads less traveled by.

Friday, December 9, 2011

Math problems of the week: final algebra problems from the 1900s vs. the 21st century

I. The final problem in Wentworth's New School Algebra, published in 1898:

Find by a graph the number of real roots of:
x8 - 8 = 0
x3 - 5x2 + 8x + 14 = 0

II. The final problem in The University of Chicago Math Progject Algebra, published in 2002:

Use the table to plot the graph of the polynomial function
P(x) = 2x3 - x2- 6x

Why can you be sure that all the x-intercepts are listed in the table?

-3_ |_-45__
-2_ |__-8__
-1.5 |__ 0_
-1_ |___3_
_-.5 |__2.5
_0_ |__0__
_.5_ |__-3_
_1_ |__-5_
_2_ |__0_
_3_ |__27_

III. Extra Credit
Chicago Math students regularly use graphing calculators; 1900's math students didn't. So why do Chicago Math students get to rely on a table for their final algebra problem?

Monday, December 5, 2011

More front-page accolades hands-on classrooms, III

From yesterday's Philadelphia Inquirer:

High school feels different in the big white mansion at the edge of the Navy Yard - no desks in rows. No 47-minute class periods. No warnings to remove the hat, put the cellphone away, take the exam seriously.

Instead, small groups of students are designing their own workshop space. They're drawing up more efficient bus routes for the Philadelphia School District. Their teachers act as mentors, sounding boards, not lecturers.

The premise? American high schools are broken.
The curriculum?
...a challenging curriculum built on student interests through hands-on projects. It means fostering strong relationships that form the underpinnings of everything.

There may be no Algebra 2 or English 4 at the workshop, but students learn the essential skills they need from those courses - solving simultaneous equations, interpreting complicated texts.
"No desks in rows"; teachers who are "mentors, not lecturers"; "hands-on projects"--why does "innovative" classroom boilerplate, ubiquitous in our "model" schools, continue to be front page news?
The current school of the week is the Sustainability Workshop, an alternative senior-year program inspired by a West Philadelphia after-school program whose students "have been building hybrid cars and winning important competitions for more than a decade" and whose members "want to turn the workshop into a full-fledged school... by 2013." Currently, 28 students attend, selected based on their attendance and behavior records. Their academic skills, one teacher says, "are all over the map."

Naturally, the school has attracted all sorts of premature attention--well before any efficacy results could possibly surface:
Three months in, the school has garnered national buzz and attracted more than $500,000 in private funding from the Barra Foundation, the Greater Philadelphia Innovation Cluster, and others.

Deep thinkers are already gushing over the workshop.
Says Andrew Zwicker of the Princeton Physics Plasma Laboratory and "associate director of education and workforce development for the innovation cluster": "It is so clearly the future of education. Or at least it should be."


Before jumping to these apparently foregone conclusions, the founders and the funders should first seek out reliable data on whether it's more effective to replace the seqential math pedagogy that is still in use by the many countries whose high schoolers outperform ours with an ad hoc "just in time" approach to advanced topics like simultaneous equations. And by reliable, I mean data that takes into account selection biases--of the sort you might find when 28 self-selected and behaviorally screened applicants opt against their typically terrible local high schools in favor of a brand new, well-funded program with a much higher (and more highly qualified) teacher to student ratio. The persistence of traditional math taught badly, as Barry Garelick has pointed out, doesn't mean we should give up on trying to teach it properly.

Saturday, December 3, 2011

How--and how not--to resuscitate the magic of childhood

One of the most common edworld justifications for spending less time on the structured teaching of core academic subjects, particularly in the early grades, is that children no longer have enough time in their lives for unstructured, imaginative play.

On this point, I'm in total agreement. For several generations now children have spent less time in yards, streets, and parks, and more time in front of screens; less time unsupervised in basements and attics and more time in scheduled, structured day cares, camps, and extra-curricular classes; less time playing games and more time doing homework (even during summer vacations); less time running around freely in open spaces and more time in adult-directed sports. And the toys that adults provide them with--from prefab minikitchens with plastic food, to verisimilitudinous costumes, to lego "kits" complete with instructions--leave hardly any room for their imaginations. Even today's playgrounds, with their uniform, space-hogging climbing structures (that more or less tell you how to play on them) and their dearth of unstructured spaces are less inspiring than they used to be. And everywhere, in our safety-obsessed, bully-vigilant society that imagines pedophiles lurking around every corner, parents are hovering in the background, ready at the drop of a hat (or the raising of a stick) to jump in and defend, moderate, or turn even basic block playing into teachable moments.

One can only wonder what this means for the happiness--and stress levels--of today's children, not to mention the memories they will take away from childhood. What about their capacity for imagination and creativity; their ability to socialize in unstructured, unscripted situations? What about their symbolic reasoning skills? If all their "imaginative" toys resemble the real things, what will inspire them to imagine an oblong block as a telephone or a cardboard box as a cave?

But does the remedy lie in altering what happens in our elementary school classrooms--specifically, in having children spend less time in structured, teacher-directed math and reading activities? Much of the problem, after all, is in what's happening--or not happening--after school, and (reluctant though people are, especially those in the business, to realize this) there's a limit to what schools can do about broader societal problems. Indeed, in their drive to be all things to "the whole child," schools have already seriously compromised our children's academic and vocational futures.

But there are ways in which schools can help a great deal. Preschools and kindergartens should toss out the minikitchens and costumes, replacing them with more plain wooden blocks and nonspecific dressups. They should also increase the time allotted for unstructured activities, and, along with all of the rest of the elementary school grades, increase recess by 300% (and stop, stop, stop using recess deprivation as a punishment). And--I've said this before--our K8 classes should almost as drastically decrease the homework assignments, eliminating all those high-ratio-of-effort-to-learning projects and Reform Math problems, and assigning no homework at all to children in grades K-3, and no summer vacation homework to anyone. Finally, they should eliminate the computers (and all other video playing devices, and all the movies and "educational videos" that go with them) entirely from our classrooms--except as tools for teaching kids how to program computers. But that's a whole nother story.