Did local control ever exist?

I went to a school board meeting two years ago, where the topic of the middle school English curriculum came up.

The English curriculum is a chronic source of woe and has been for as long as we've lived here, which is sixteen years now.

Come to find out, parent unhappiness with the English curriculum goes back at least as far as 35 years. After I stood up and commented on the fact that we still do not have a required reading curriculum that includes the classics (here's what we do have), a member of the board said that his own mother had been unhappy about it, too.

That would have been around 1980.

When did public schools start hiring exclusively from ed schools?

Another year, another school board election

My district has been constructivizing itself for 16 years now, and people have yet to catch on.

• Constructivism isn't working
• Education schools don't teach teachers how to teach
• Shark Tank
• Peter Meyer weighs in

Younger

As the nation's schools undergo a wave of teacher retirements, some 25% of teachers have only five or fewer years in the classroom, "a precipitous decline" in experience since the late 1980s, when the typical teacher had 15 years' experience, according to a study by the National Commission on Teaching & America's Future, a Washington, D.C. nonprofit advocating teacher quality.

That may explain why some 43% of parents report being "extremely worried" about their kids' elementary-school teacher assignments, according to a poll last month of 306 parents by CafeMom, a social-networking and community website.

Dread of August: The Kids' Teacher Assignments | By SUE SHELLENBARGER | Aug. 6, 2013

This generation of teachers has been trained in pure constructivism.

According to Robert Slavin, direct instruction hard been all but dropped from teacher training by 1991.

Is the S finally hitting the fan?

From Allison, on EngageNY:

The problem is the name has changed, but the song remains the same.

Common Core is the new "new Math", unfortunately the umbrella name for everything happening in math ed these days as the standards get put in place, including things that really have nothing to do with standards.

The Common Core State Standards were, and are, a set of standards. Standards are lists of requirements. It's true that CCSSI were more proscriptive than typical standards, but they were still just standards. Standards are not curriculum. For more on this, see my post.

The CC standards in k-8 are better than NY's previous standards. That is about the end of the good I can say in NY's implementation of the new standards.

For whatever reasons, probably largely related federal funding, states adopted CCSS. Except they did so before any textbooks had been written. And before the assessments against the standards had been written.

So NY schools and teachers were supposed to magically teach from the new standards about which they had been told nothing, or use hastily repackaged curricula that wasn't really changed, or who knows what.

But help was on the way! Engage NY was created! It would be an entire curriculum online, free to everyone, digital! No need for textbooks! Isn't that great? And famous mathematicians and math teachers who are pro Singapore math had signed up to lead the writing of the curriculum on EngageNY.

At some point last spring, I saw several job reqs from EngageNY. They needed curriculum writers. I considered taking the position. Then I looked at what was already on EngageNY.

I saw a fraction lesson that was fundamentally wrong from beginning to end. I saw other lessons with equally egregious errors. I told someone who told someone high up at EngageNY. The response was, yes, it's wrong, and the writer was informed, but the writer could not understand what was wrong with it and refused to rewrite it, saying they knew it was better for kids this way.

EngageNY is still beholden to the same NYS ed people. The math people who were supposedly leads don't control the curriculum; the bureaucrats do, and are actually telling the math people what the scope and sequence must be.

This is now all called "Common Core."

Given the difficulty of the Common Core tests, I wonder if we'll see so many parents up in arms that .... that school boards will finally have to wake up.

Till now, the math warriors in any community were always a minority, but now everyone's child is failing math.

That said, here in Irvington sentiment in the one and only survey ever taken on the subject, was around 80% anti-Trailblazers, and the board still voted to reject Singapore Math & keep Trailblazers.

Of course, the Interim Curriculum Director announced at the time that the survey was favorable to Trailblazers. She also announced, again, that the Parents Forum (me) had misled the public.

I always enjoyed that, sitting in the audience at school board meetings, being slandered via innuendo.

Or is that libeled?

I never remember which is which.

I learned the legal meaning of the word innuendo through direct personal experience of innuendo about me, purveyed by sitting members of the school board and by central administrators.

I'm going to go read the link Allison left to Wu's piece now.

must-see TV: Common Core edition

woo hoo!

old wine, new bottle

"The Death and Life of the Great American School System"

Ravitch suspects, with good reason, that her favorite teacher, the intelligent, exacting, and highly literary Mrs. Ratliff, would languish under NCLB. But would Mrs. Ratliff even have become a teacher in today's world? Would someone who is "stifled by the jargon, the indifference to classical literature, and the hostility to her manner of teaching" last through even one week of ed school pabulum, projects, peer-group activities, and proselytizing about Balanced Literacy?

An excerpt of my review of Diane Ravitch's latest book at the Nonpartisan Education Review. You can access the entire review here.

In this book Ravitch brings up her next most recent book: The Language Police. Intrigued (and embarrassed that I hadn't yet read it) I devoured that one a few days ago. If you haven't read it yet, it's a great read.

missing knowledge

Barak Rosenshine on teacher effectiveness research:

I suggest that the teacher effects era, between 1955 and 1980, was an impressive run of cumulative research. During this period, over 100 correlational and experimental studies were conducted using a common design and the different observation instruments shared many common instructional procedures. And it was cumulative: researchers cited and built upon the instructional findings of others.

After several years of immersion in the education world, I am just now finding out about this.

Return of the repressed.

chemprof on what ed schools teach

ChemProf said...

"exactly what do ed schools purport to teach?"

From an ed school, here are six principles they purport to teach:

Working in education is a moral act based on an ethic of care.
Working in education is a collegial act.
Working in education is reflective and inquiry-based.
Working in education is a political act.
Working in education is acquisition of subject matter and professional knowledge.
Learning is a constructivist and developmental process.

Notice -- nothing about classroom management, discipline, student achievement, or fundamentals. Lots of philosophy of education, constructivism, and (buried in the principles) diversity. At my own school, I've been to admission events with folks from the ed school. Things they talk about: reducing the achievement gap, making sure to teach history students about the genocide of American Indians and similar politically correct stuff. Things they don't: gifted students, subject matter, science/math education, actually teaching.

I'm afraid I have to agree with Barry -- this book won't crack the ed school shell. It is just too thick.

a picture is worth a thousand words

from chemprof:

In the "it is always worse than you think" category, I had someone from the education department recently tell a story where she expressed frustration with a kid for trying to sound out the word when "the picture is right there." Why they think this teaches reading is beyond me.

Susan Engel's revolutionary new proposals for education reform

In an Op-Ed in yesterday's New York Times, Susan Engel, a senior lecturer in psychology and the director of the teaching program at Williams college, makes the bold proposal that "if we want to make sure all children learn, we will need to overhaul the curriculum itself." Almost as original as Engel's proposals is her original use of language, some of which I've put in bold face.

"Our current educational approach," Engel argues, "is completely at odds with what scientists understand about how children develop during the elementary school years and has led to a curriculum that is strangling children and teachers alike."

In particular, students shouldn't be spending "tedious hours learning isolated mathematical formulas or memorizing sheets of science facts that are unlikely to matter much in the long run."

Engel proceeds to enlighten us on the following things that "scientists know" and that "research has shown unequivocally":

-children "construct knowledge; they don't swallow it."

-"the first step to literacy is simply being immersed, through conversation and storytelling, in a reading environment"

-"the second [step to literacy] is to read a lot and often."

-"people write best when they use writing to think and to communicate rather than to get a good grade."

-"children learn best when they are interested in the material or activity they are learning."

-collaboration is "a skill easily as important as math or reading."

Based on these astonishing new insights from science, Engel boldly proposes the following paradigm-shattering changes to classrooms:

-every child should be given "ample opportunities to read and discuss books."

-children should "spend an hour a day writing about things that have actual meaning to them--stories, newspaper articles, captions for cartoons, letters to one another."

-children should "spend a short period of time practicing computation" and once they are "proficient in those basics they would be free to turn to other activities that are equally essential for math and science: devising original experiments, observing the natural world and counting things, whether they be words, events, or people." (Children love such activities, Engel argues, "if given a chance to do them in a genuine way").

-children should engage in playful activities "from building contraptions to enacting stories to inventing games," which will "help them acquire higher-order thinking skills like generating testable hypotheses, imagining situations from someone else's perspective and thinking of alternative solutions."

-children should have ample time "to collaborate with one another."

Clearly Engel not only knows her cognitive science, but has spent countless hours observing what happens in today's classrooms: all that futile phonics instruction; all those tedious math and science drills; all that dearth of collaborative learning, game playing, letter writing, and cartooning.

But I must reserve my greatest appreciation for the New York Times for deeming it fit to publish this courageous piece, with its original criticisms of today's classrooms, its revolutionary proposals for reform, and its pioneering attempts to bring science into classroom teaching (Dan Willingham, please take note!).

advice for curriculum committees everywhere

We've got so much going on here in town (posts t/k) that I'm only dimly aware of what is or is not happening at state & federal levels .... so I was surprised to discover this Daily News editorial yesterday while paging through looking at whatever it was I was looking at post-tennis lesson, no less.

I assume this is what they're referring to.

The Regents are authorizing the development of a performance-based approach to teacher certification and inviting – on a trial basis – new entities to prepare teachers for certification. As part of this new approach, the Regents will support the development of new performance-based assessments for teacher certification (including the eventual use of value-added assessment as a component of professional certification), will develop new methods to recruit and retain teachers for high needs schools in subject shortage areas and will allow additional content knowledge demonstrations for prospective teachers to bring new talent into the teaching field.

I'm interested to hear from teachers on this.

I would dearly love to see different teacher training programs (I'm guessing most teachers would dearly love to see different teacher training programs), and I think David Steiner is the person to do that.

But why does Kendall Hunt get off scot-free?

Or Heinemann?

Shouldn't these folks have to show a value-added value or two?

I guess this is a policy question, really. Targeting teacher-ed programs seems like a good idea to me. At least, it's a reasonably novel idea -- and I think that, historically speaking, a reform effort directed at medical schools may have had an enormous effect (yes?)

Data is good; value-added is good. In my view.

But targeting teacher ed programs and pushing through value-added measurements without reference to New York state's vendor-driven curricula is a different matter.

Have I ever mentioned my rule of thumb for school districts buying curricula?

Buy whatever homeschoolers are buying.

"Are Teacher Colleges Producing Mediocre Teachers?" TIME

TIME article by Gilbert Cruz.

Are Teacher Colleges Producing Mediocre Teachers?

OK, but is there anything constructive or promising here?

The article was based on a speech by Arne Duncan on Thursday to Columbia University's Teachers College. Duncan said:

"By almost any standard, many if not most of the nation's 1,450 schools, colleges and departments of education are doing a mediocre job of preparing teachers for the realities of the 21st century classroom,"

"By almost any standard."

{I'll ignore the 21st century remark.]

Then, Cruz quotes David Steiner, New York's education commissioner as saying:

"And if we can't identify the skills that make a difference in terms of student learning, then what we're saying is that teaching is an undefinable art, as opposed to something that can be taught."


"Until recently, Steiner served as dean of Hunter College's School of Education, where he was a vocal critic of the typical ed-school approach, in which teachers-in-training study theories and philosophies of education at the expense of practical, in-the-classroom experience."

Then Duncan is quoted as saying:

"I am urging every teacher-education program today to make better outcomes for students the overarching mission that propels all their efforts."

But what is the "standard" that should be used? It's one thing to argue mediocrity "by almost any standard", but there has to be some agreement over what that standard should be. The only standard that seems to be available is a mix of 50 state standards - all low. Some apologists of bad results complain that the bad scores on the tests mean that the tests are fundamentally flawed or that the schools didn't teach the specific material of any particular question. Apparently, these people are quite capable of arguing the "by almost any standard" position.

But the problem is not just poor implementation and a lack of focus on outcomes. It's philosophy. It's low expectations. The problem is that people disagree on standards. We can't even get started.

Actually, I'm more encouraged by Duncan's arm-twisting in states to force them to open up more charter schools. I can't imagine a top down solution to the problem of education that won't be watered down or manipulated. Either parents have to be allowed to send their kids elsewhere, or schools have to provide parents with choice. TERC or Singapore Math. I don't expect the education world will give up control easily. They will accept (low) accountability and weak standards first.

down and out in San Diego

from the Weekly Standard:

There he was, Bill Ayers himself, sitting in a Marriott conference room waiting to partake in a session of the annual meeting of the American Educational Research Association (AERA).

[snip]

[H]e is something of an AERA celebrity these days, having been elected vice president of its curriculum-studies division--which specializes in research on what teachers teach, both at the ed-school level and in the K-12 classrooms where most ed-school graduates find employment. He participated in no fewer than seven panels and events at this year's convention. AERA, by the way, with 25,000 members, is the leading scholarly organization for professors at U.S. education schools--the people who teach the teachers who teach your children. Its annual meeting drew nearly 14,000 people to the San Diego Convention Center in April.

[snip]

At this particular session, titled "Public Pedagogy and Social Action: Examinations and Portraits," Ayers was chairman of the panel.

[snip]

The room quieted when William Schubert, a black-clad, armband-wearing fellow education professor at Illinois-Chicago, introduced the social-action theme of the session by declaring, "The project of education is the project of composing a life."

After a few dismissive words apparently aimed at the practice of requiring education majors to obtain a basic arts-and-sciences grounding alongside their pedagogic fare, Schubert introduced the first panelist, Jennifer April Sandlin of Arizona State. Her research had consisted of email interviews with Reverend Billy, an Elvis-haired anti-Wal-Mart street preacher who is currently running as Green party candidate for mayor of New York and whom Sandlin presented as an example of public pedagogy.

Sandlin's interview questions, laminated in triple-clad academic jargon, had evidently flummoxed Reverend Billy. "Why don't you professors stop leaning further and further into your private world?" he had complained in an email to Sandlin. Her explication of the preacher's message, aided by her coresearcher, Jake Burdick, included the following words and phrases: "bounded space," "reinscribe," "alterity," "counter-hegemonic," "imperialistic legacy," "Euro-Western perspective," "polymodal discourse," "the politics of representation," "reflexivity of discomfort," "legitimization," "colonized," "transgressive," and "the dialogic process of being human." I knew how Reverend Billy felt.

[snip]

Finally Ayers rose to speak--delivering an impromptu-sounding ramble that had little to do with murals or creativity in classrooms. He named his two heroes: "Martin Luther King and Harvey Milk." He voiced dialectical doubts: "Multicultural education started in insurgency against pedagogical racism," he declared. "Then it became the new norm. We have to ask: What are the dogmas that we're creating now?"

On that last point I was in hearty agreement.

math wars

During my four days at the AERA meeting, I vainly searched for a single session whose panelists expressed some dissent from the baseline principle of progressive education: that teachers shouldn't directly impart information to their students but instead function as "guides," gently coaching them to "construct" their own knowledge about the subject at hand out of what they already know or don't know.

"Everyone here is a constructivist," Gabriel Reich, a genial education professor at Virginia Commonwealth University, told me at a reception sponsored by the John Dewey Society. (Dewey, a pragmatist philosopher who died in 1952 and taught for years at Columbia Teachers College, is regarded, alongside the Swiss cognitive psychologist Jean Piaget, as one of the fathers of progressive education.) Reich was trying to explain to me why it was presumptuous for professional mathematicians (and many parents) to be up in arms about the currently fashionable constructivist idea that instead of explaining to youngsters, say, how to do long division, teachers should let them count, subtract, make an educated guess, or otherwise figure out their own ways to solve division problems. College math professors may complain that young people taught the constructivist way arrive in their classrooms unable to perform the basic operations necessary to move on to calculus, but so what? "Why should we privilege professional mathematicians?" Reich asked. Long division, multiplication--"those are just algorithms, and a calculator can do them faster than we can. Most of the people here at this meeting don't think of themselves as good at math, and they don't think math is creative. [The constructivist approach] is a way to make math creative for many people who never thought of it that way."

There are no wrong answers in constructivist theory, so Reich, pursuing his mathematical theme, had a tough sell the next day when he presented a paper to his fellow educators arguing that the principles of constructivism should be modified a bit in teaching arithmetic. "I know some constructivists might take issue with what I'm saying," was his delicate way of telling his audience that when a student says two and two equals five, there might be a problem, if only with the child's non-constructivist parents who might have "right-answer" concerns. Reich was suggesting that the youngster's incorrect (or "incorrect") answer be "vetted by the class" to see if it "works." That way, he explained, "the students are learning to act as members of a mathematical community--they are becoming mathematicians."

and PowerPoint

Another session, titled "Teaching and Assessing 21st-Century Skills," was premised on the idea that schools ought to focus, not on imparting content--such as history, science, and so forth--but on getting their students up to speed on how to function in the fast-changing employment market of the 21st century by learning how to use computers and how to work with their fellows on a "project" (that is what people do at their jobs nowadays, isn't it?). Once young people get their 21st-century skills down, the thinking goes, they can learn and plug in whatever specific knowledge they need: math, physics, and engineering if they're designing a bike path, and so forth. Addressing an audience of nearly a hundred people (a huge crowd for AERA), the six advocates for "project-based learning," as it is called, fairly bristled with Dilbert-esque office lingo as they urged teachers to turn their classrooms into replicas of technology-intense workplaces: "deliverables," "teamwork," "feedback," "use cases," "design patterns," "meta-cognitive," "framing," "the next level of learning." They had also mastered that 21st-century skill par excellence: the PowerPoint presentation, read aloud line by line and bullet point by bullet point. Indeed, a PowerPoint screen displaying a verbatim version of the speech plus more bullets than flew at the St. Valentine's Day Massacre was a feature of nearly every AERA session I attended.

reform, too

At the AERA sessions, I lived in an ideological Bizarro World in which "school reform" did not mean improving classroom instruction but rather, handing over multimillion-dollar state grants (in Illinois) to the control of, among other entities, the Association of Community Organizations for Reform Now (ACORN)--a group being prosecuted for alleged voter-registration fraud in the 2008 election--so that ACORN can help direct the subsidization of the candidates of its choice for ed-school training. It was a world in which at a session on Queer Theory, one teacher-panelist announced, "I'll sometimes ask my students, 'Why can't a girl have a penis?' and you know, they start asking themselves the same question: Why can't a girl have a penis? Why can't a girl with a penis wear a skirt?"
'Why Can't a Girl Have a Penis?' and other major issues in educational research.
by Charlotte Allen
05/18/2009, Volume 014, Issue 33

They're none too keen on Teach for America, either.

what is indirect instruction?

now you know

missed the memo

End of the reading wars.

In the past seven years, a new view of reading instruction has taken hold in school districts nationwide.

The issue these days isn't whether "phonics" or "whole language" is the better approach for beginning readers, but how to blend those philosophies and other elements in a reading program tailored to the individual child.

For a growing group of educators, the reading wars, waged so ferociously in the 1980s and '90s, are past. Or at least passe.

"I think more schools are moving toward a balanced literacy program," said Tina Chekan, co-principal and literacy coach at Propel McKeesport, a charter elementary school. Propel also operates elementary schools in Homestead, Kennedy and Turtle Creek.

"There's not one program that fits all," she said. "We know that our students are on varying ability levels. We work to really focus on the individual."

[snip]

Some educators now downplay the significance of the reading wars, calling them the over-publicized rants of academic extremists. Dr. Roller, of the International Reading Association, considers the wars a dead issue.

"I wish somebody would hold a big funeral service and bury this casket," she said.

I don't think that's going to happen. 

means of transmission

EDUCATION trends have three means of transmission, all invisible to the public: the sale of textbooks and other instructional materials, teaching in schools of education, and teacher-training seminars conducted during the paid noninstructional days that are provided in teachers' contracts. As superintendent in California, [Bill] Honig realized that he couldn't directly affect what was taught in schools of education, because they are independent of the state board of education, and so if he wanted to have any real influence over what went on in public-school classrooms, the best means at hand were textbooks and seminars. He moved aggressively to put his people in charge both of setting up California's eight annual "staff development" days for teachers and of writing state subject-matter "frameworks," which form the basis for textbook orders.

The Reading Wars by Nicholas Lemann

Atlantic Monthly November 1997

Thus was born the California Subject Matter Project. Ed headed the History Social Science Project; Phil Daro, currently a member of the mathematics Work Group for the Common Core national standards effort, was in charge of the Mathematics Project.

The Subject Matter Projects gave teachers professional development in the form of seminars taught by disciplinary specialists. History teachers took seminars given by history professors, not consultants. Ed says today that, at the time, he had no idea how radical Honig's concept was.

Me, neither.

book learning

71% see book learning as key to success

Fifteen percent (15%) say street smarts are more important, and 14% are not sure which is better.

[snip]

More than eight-out-of-10 adults who earn more than $75,000 per year say book learning is more important than street smarts, higher than for any other income groups.

I'd love to see this question asked of a) classroom teachers, b) administrators, c) education school professors, d) educational consultants, and e) VENDORS. I'm guessing teachers would be much closer to the public than the other three.

In any event, the fact that 71% of the public thinks book learning^* is the secret to success while 86% of education professors told Public Agenda that, "The process of learning is more important ... than whether or not students absorb specific knowledge," tells you parents and taxpayers need a vote. A vote and a veto, preferably.


the struggle

While I'm constructing my survey wish list, I'd like to know how many parents would sign off on this sentiment:

Nearly 9 in 10 (86%) say when K-12 teachers assign math or history questions, it is more important for kids to struggle with the process of finding the right answers than knowing the right answer.

students must struggle

^* I am assuming that by "book learning" parents mean learning and remembering, i.e. the acquisition of knowledge

palisadesk on guerilla instructivism

You talk about a long list of readiness characteristics in your district, but what about ed schools? You talk about a long list of readiness characteristics in your district, but what about ed schools?

In my area the 2 major ed schools focus on "big ideas" like diversity, social justice and being a change agent. They don't concern themselves with any practicalities, like how to teach anybody anything.

I surveyed the new teachers and the army of student teachers coming into our school over the last decade and they all report learning nothing about assessment, classroom management, cognitive or behavioral science, early reading/literacy, communicating with parents or indeed much of anything of a practical nature. They study Paulo Friere, Jonathan Kozol, Sylvia Ashton-Warner,^* and so on. The content is nearly all theoretical and philosophical, nothing empirical, evidence-based or useful on the classroom level.

This is not all that unusual a situation. In many areas it is the district that teaches new teachers what to do and provides workshops and non-credit courses on balanced literacy, how to administer the Developmental Reading Assessment, do Writers Workshop and Guided Reading, and so on. The mandate for these practices comes not from the Ed schools but from the district level and from the department of education level higher up. I haven't seen any evidence that ed schools set the agenda; they seem to be responsive to what the education bureaucracy wants -- in many cases, ed school staff are bureaucrats as well, sometimes on assignment for a 2-5 year stint at an ed school, other times they hold double assignments. It's one big cabal running both the ed schools and senior management in the bureaucracy.


An even more cynical blogger might take away that by pushing these literacy skills down to parents' responsibilities, it leaves teachers free to give Writer's Workshop instead.

I find that many parents and private citizens do not know this, so I will point it out: teachers are not, in most jurisdictions, "free" to give or not give Writers Workshop, or Guided Reading, or whatever curriculum practice is the latest craze. Most districts are quite prescriptive and require teachers to comply with very specific guidelines -- what materials they may (and may not) use, what practices they MUST employ (Word Walls, Writers Workshop, Readers Workshop, Guided Reading, Shared Writing, and so on). They may be specifically forbidden to do other things (teach standard algorithms, teach systematic phonics, hold students accountable for spelling, meeting deadlines, completing assignments). Many districts have "literacy police" (even "numeracy police") who go around inspecting classrooms and monitoring compliance. Teachers have very little freedom in most districts to choose their own methods or materials. That has both positive and negative consequences.

The infatuation with most of the practices so often deplored here (and elsewhere) does not come from teaching staff but from higher up in the bureaucracy. Indeed, surveys have shown almost as great a disconnect between what teachers want and think effective vs. what administrators and bureaucrats want/believe as the Public Agenda study "Different Drummers" showed exists between ed school faculty and the public at large, including teachers. There is a great divide, but the power is largely on one side.

Being a successful "guerrilla instructivist" requires camouflage and using the opposition's terminology and jargon to describe things totally incongruent with the prevailing philosophy. One can generally assume ignorance of instructional matters, research and cognitive science on the part of school and district administration, so unless you wave red flags in front of them they will not notice the details of what you do as long as you appear assertively compliant.

What would we do without palisadesk (and redukudu & Paul B & Instructivist & Concerned ....)?

That is not a rhetorical question.

What these teachers do for children, families, and for their country goes far beyond guerilla instructivism. I was about to invoke the samizdat, but that's not quite right, is it? This is America; palisadesk has a right to speak her mind, although if she were to do so using her own name she would put her job at risk.

I've just asked Ed whether there is a historical precedent for this kind of 'inside reporting.' He says that during the Ancien Regime there were members of the court who, using a pseudonym, wrote about court intrigues and the like.

But that's all he could think of on the spur of the moment.

The writings of guerilla instructivists make me wonder whether the internet really is something new and different: whether the internet has a "democratizing" effect in realms that have been anything but democratic.

We will see.

handing it to the student

By way of introduction, I am neither mathematician nor mathematics teacher, but I majored in math and have used it throughout my career, especially in the last 17 years as an analyst for the U.S. Environmental Protection Agency. My love of and facility with math is due to good teaching and good textbooks. The teachers I had in primary and secondary school provided explicit instruction and answered students’ questions; they also posed challenging problems that required us to apply what we had learned. The textbooks I used also contained explanations of the material with examples that showed every step of the problem solving process.

I fully expected the same for my daughter, but after seeing what passed for mathematics in her elementary school, I became increasingly distressed over how math is currently taught in many schools.

Optimistically believing that I could make a difference in at least a few students’ lives, I decided to teach math when I retire. I enrolled in education school about two years ago, and have one class and a 15-week student teaching requirement to go. Although I had a fairly good idea of what I was in for with respect to educational theories, I was still dismayed at what I found in my mathematics education courses.

In class after class, I have heard that when students discover material for themselves, they supposedly learn it more deeply than when it is taught directly. Similarly, I have heard that although direct instruction is effective in helping students learn and use algorithms, it is allegedly ineffective in helping students develop mathematical thinking. Throughout these courses, a general belief has prevailed that answering students’ questions and providing explicit instruction are “handing it to the student” and preventing them from “constructing their own knowledge”—to use the appropriate terminology. Overall, however, I have found that there is general confusion about what “discovery learning” actually means. I hope to make clear in this article what it means, and to identify effective and ineffective methods to foster learning through discovery.

To set this in context, it is important to understand an underlying belief espoused in my school of education: i.e., there is a difference between problem solving and exercises. This view holds that “exercises” are what students do when applying algorithms or routines they know and the term can apply even to word problems. Problem solving, which is preferred, occurs when students are not able to apply a mechanical, memorized response, but rather have to figure out what to do in a new situation. Moreover, we future teachers are told that students’ difficulty in solving problems in new contexts is evidence that the use of “mere exercises” or “procedures” is ineffective and they are overused in classrooms.

As someone who learned math largely though mere exercises and who now creatively applies math at work, I have to question this thinking. I believe that students’ difficulty in solving new problems is more likely to be because they do not have the requisite knowledge and/or mastery of skills—not because they were given explicit instruction and homework exercises.

Those who make such a differentiation and champion “true” problem solving espouse a belief in having students construct their own knowledge by forcing them to make connections with skills and concepts that they may not have mastered. But, with skills and concepts still gelling students are not likely to be able to apply them to new and unknown situations. Nevertheless, the belief prevails that having students work on such problems fosters a discovery process which the purveyors of this theory view as “authentic work” and the key to “real learning.” One teacher with whom I spoke summed up this philosophy with the following questions: “What happens when students are placed in a totally unfamiliar situation that requires a more complex solution? Do they know how to generate a procedure? How do we teach students to apply mathematical thinking in creative ways to solve complex, novel problems? What happens when we get off the ‘script’?”

Discovery learning in math: Exercises versus problems (pdf file)
by Barry Garelick
THIRD EDUCATION GROUP REVIEW / ESSAYS, Vol.5, No.2, 2009

make them struggle
education professors: students must struggle
KUMON: "work that can be easily completed"
handing it to the student

another nail in the coffin

Is Traditional Teaching Really All that Bad?

answer: no