Posts
I have moved from more self-indulgent beliefs about the free development of children in general, to a certain knowledge of my personal responsibility for the future well-being of one child in particular: my child.
This past week I took a short tour of constructivism led by D.C. Phillips. Who is quite sympathetic to constructivism. But it was a great tour. It had everything, epistemologically speaking: the good, the bad, and the ugly.
Then I took a short tour of the not-so-subtle difference between finding out and making sense led by Michael R. Matthews. I found out that I prefer the discovery of truth to its invention (or construction).
I am now a true believer in discovery learning; it's just that I want it to happen very fast. Which means directly telling my child what I want him to know, what I want him to do to know, and when he should do it to know it. Life is short, in other words, and truth is external to my child.
I can now tell the difference between a radical constructivist,
"every man for himself"
a social constructivist,
"every culture for itself"
and a realist.
"we are all in the same boat"
I think I am a realist.
The post title is a quote from Devitt, who writes elsewhere,
Here is a summary of my argument for Realism. I start by observing that Realism about the ordinary observable physical world is a compelling doctrine. It is almost universally held outside intellectual circles. From an early age we come to believe that such objects as stones, cats, and trees exist. Furthermore, we believe that these objects exist even when we are not perceiving them, and that they do not depend for their existence on our opinions nor on anything mental. This Realism about ordinary objects is confirmed day by day in our experience. It is central to our whole way of viewing the world, the very core of common sense. Given this strong case for Realism, we should give it up only in the face of powerful arguments against it and for an alternative. There are no such arguments. That concludes the case for Realism.
Stones, cats, and trees. And my child. I am satisfied.
18 comments:
Thanks for this post and the link to the DC Philips paper. I'm doing a presentation for my class in ed school about "social constructivism" (it was one of the topics to choose from) and his paper was cited in another paper that criticized problem-based or discovery learning (by Kirschner, Sweller and Clark, talked about here and on D-ed Reckoning).
I agree with your observations. Constructivism holds that learning occurs when knowledge is constructed and most psychologists agree with that. Anderson, Reder and SImon (1998) (don't have the link yet, sorry) say that's no big deal and that in fact, learning is constructed both passively (i.e., by direct instruction) and actively (discovery, problem-based, inquiry-based, etc). Someone posted a comment saying it was a continuum--I'm calling it a spectrum in my presentation. At one end is direct instruction, and at the other is pure discovery. I grew up being taught using guided discovery that was closer to the direct instruction side of the spectrum. I think most of us did.
Other empirical studies I've read show that "naive learners" (i.e., those with little or no domain knowledge in what is being learned) do well with direct instruction, but those with some domain knowledge do better on the discovery side of the spectrum. The problem with many of the math programs in the way they're put together and taught is the assumption they make about students' prior knowledge. There's a feeling of "Oh yeah, they can make the connection between what we want them to discover and what they already know." What happens has been talked about ad infinitum on various web sites. You get a three ring circus of new information going on in the kid's head and they hit cognitive overload. They can't make sense of anything. Sure, kid, here's a rectangle with the area of x^2 + 5x + 6. Can you find the two sides of the rectangle? What, you haven't had factoring? Now's a good time to learn. (No joke, folks, this is an approach that CMP uses in their unit on quadratic equations called "Frogs, Fleas and Painted Cubes".
"I agree with your observations. Constructivism holds that learning occurs when knowledge is constructed and most psychologists agree with that. Anderson, Reder and SImon (1998) (don't have the link yet, sorry) say that's no big deal and that in fact, learning is constructed both passively (i.e., by direct instruction) and actively (discovery, problem-based, inquiry-based, etc)."
I cannot understand for the life of me how construction and discovery can be compatible. If knowledge is just lying around the kitchen table or on the floor to be discovered, then why does it need to be constructed? If it is to be constructed, why does it need to be discovered?
I can understand construction in the banal sense that we must somehow integrate external input (from observations, books, sage on the stage, etc.) into our knowledge apparatus, but the external input must still be there. This type of integration is necessarily always active, contrary to educationist palaver. So-called "constructivists" militate against this external input and disparage textbooks, explicit and expository instruction, etc.
My own favored teaching/learning model is one I dubbed the Optimal Electrode Gap model, or OEG model (somehow I feel I must turn this into an acronym. Acronyms lend legitimacy even to screwball ideas. Not that I consider the OEG model to be a screwball idea).
The analogy is taken from physics. When relatively high voltage is applied to electrodes, three things can occur depending on the electrode gap:
a) no sparks fly if the electrodes are too far apart
b) a short-circuit is created if the electrodes touch each other
and c) sparks begin flying if the gap is just right.
This technical bit lends itself beautifully as an analogy and even metaphor for education where it has major implications for teaching and learning. The flying sparks are a metaphor for true learning and understanding. The electrode gap stands for the kind of pupil/teacher interaction. Finding the right gap is at the heart of a teacher's teaching ability and skill.
If a teacher talks above the head of the pupil without connecting with the pupil's prior knowledge, then the gap is set too wide and no sparks fly. If the teacher tells the student (who may not be paying attention as is most often the case) everything without allowing for creative tension and some student struggle, then we have a short-circuit (the electrodes touch each other) and the voltage is for nought.
On the other hand, finding the right gap prevents pupil frustration on the one hand and wasted energy on the other, and can lead to student excitement and enthusiasm, and a real sense of accomplishment.
This is my teaching philosophy in a nutshell. I am not sure how all of this ties in with prevailing theories, but I suspect it incorporates elements from a variety of philosophies.
Yes, the spark gap analogy is quite good. It fits in with the Vygotsky theory of Zone of Proximal Development or ZPD. You want to teach children in that zone (i.e., the spark gap is not too wide) and provide the scaffolding or guidance to help bridge that gap.
With respect to your question:
I cannot understand for the life of me how construction and discovery can be compatible. If knowledge is just lying around the kitchen table or on the floor to be discovered, then why does it need to be constructed? If it is to be constructed, why does it need to be discovered?
I'm afraid I misstated something. I meant to say learning --even via direct instruction--requires active participation by the learner and is NOT passive learning as is the accusation levied by the radical constructivists. I was referring to a paper by Anderson, Reder and Simon called "Radical Constructivism and Cognitive Psychology" which appeared in a collection published by Brookings Institute in 1998. In the paper, they state:
“A consensus exists within cognitive psychology that people do not record experience passively but interpret new information with the help of prior knowledge and experience. The term “constructivism” is used in this sense in psychology, and we have been appropriately referred to as constructivists (in this sense) by mathematics educators. However, (AND THIS IS A BIG ‘HOWEVER’ FOLKS) denying that information is recorded passively does not imply that students must discover their knowledge by themselves without explicit instruction, as claimed by radical constructivists. In modern cognitive theories, all acquisition of knowledge, whether by instruction or discover, requires active interpretation by the learner. The processing of instruction can be elaborate, its extent growing with the amount of relevant knowledge the learner brings to the task.”
Which I think is what you meant by "the external input must be there".
The link to the Anderson, Reder, Simon paper is:
http://act-r.psy.cmu.edu/papers/145/98_jra_lmr_has.pdf
Barry - I found the How People Learn quote on ktm 1.
A common misconception regarding 'constructivist' theories of knowing (that existing knowledge is used to build new knowledge) is that teachers should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves. This perspective confuses a theory of pedagogy (teaching) with a theory of knowing. Constructivists assume that all knowledge is constructed from previous knowledge, irrespective of how one is taught (e.g., Cobb, 1940)--even listening to a lecture involves active attempts to construct new knowledge.
How People Learn
This type of integration is necessarily always active, contrary to educationist palaver.
One thing I've been noticing about our administrators here is that they don't seem to read much. At least, they never mention books they've been reading; our libraries are short books; we are missing textbooks, etc.
The new assistant super opened her meeting with unhappy parents by citing 3 books she'd read recently that had influenced her. This bowled Ed over.
That was the first time he'd ever heard an administrator mention a book that had influenced her.
If you don't "read to learn" you might not be aware of how much effort it takes to learn through reading.
When I gave the middle school principal some material to read he groaned.
"More reading."
direct quote
"A common misconception regarding 'constructivist' theories of knowing (that existing knowledge is used to build new knowledge) is that teachers should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves."
I get the feeling that this misconception is the rule in edland. Someone should tell educationists that they are laboring under a misconception.
"This perspective confuses a theory of pedagogy (teaching) with a theory of knowing."
Maybe so, but educationists are quick to point out that this theory of knowing has implications for a theory of pedagogy. Hence the disparagement of external input.
Constructivism is undoubtedly a major theoretical influence in contemporary science and mathematics education. Some would say it is the major influence. In its post-modernist and deconstructionist form, it is a significant influence in literary, artistic, history and religious education. Constructivism seemingly fits in with, and supports, a range of multicultural, feminist and broadly reformist programmes in education. Although constructivism began as a theory of learning, it has progressively expanded its dominion, becoming a theory of teaching, a theory of education, a theory of the origin of ideas, and a theory of both personal knowledge and scientific knowledge. Indeed constructivism has become education’s version of the ‘grand unified theory’.
I love it!
I've just "discovered" something fantastic!
In 1997 Norway mandated constructivism in all of its schools.
At the same time it also mandated an extra year of schooling.
Part of the constructivist mandate was that 60% of the day be devoted to "thematic" (interdisciplinary) studies.
result: The country's math & science scores are a disaster.
I've been sick as a dog for the past few days, but as soon as I get back on my feet I'll pull a post together.
[There's a feeling of "Oh yeah, they can make the connection between what we want them to discover and what they already know."]
Right now I am trying to have my charges make the jump from equivalent fractions, LCM and adding fractions with like denominators to adding fractions with unlike denominators. It ain't happening. The connection could be made but isn't. Lots of teacher input and practice needed before there is any hope for a conceptual leap.
The fuzzies are hallucinating.
Barry,
you ought to check out this piece by Lomas and the response by Matthews (link will be at the bottom) if you are researching Paul Ernest and "social constructivism" as it impacts teaching practices in mathematics education.
Instructivist,
I got my boys to make the jump to adding fractions with unlike denominators by using the number line model for fractions recommended by Wu, and only after lots of experience ordering fractions. Which motivates finding the common denomination.
We started with the smallest possible unfamiliar pair, e.g. thirds and fifths. With pencil and paper, the boys and I walked through slicing each segment of length one-third into five equal pieces, and each segment of length one-fifth into three equal pieces, and so forth.
I don't like starting with the unit square area model for adding fractions -- first slicing vertically and then horizontally. I think it's confusing. Better to stick with an interval from 0 to 1 on a number line.
Yes, the spark gap analogy is quite good. It fits in with the Vygotsky theory of Zone of Proximal Development or ZPD. You want to teach children in that zone (i.e., the spark gap is not too wide) and provide the scaffolding or guidance to help bridge that gap.
It's in trying to define what constitutes scaffolding that the constructivist mischief begins again in earnest.
Constructivists deny the possibility of scaffolding by directly instructing or directly telling the child how to bridge the gap between what he knows and what we know he could know next. They allow indirect methods only, and they are even uncomfortable with presuming to know what the child should know next. They wait patiently, and they wait and wait. After all, it's not their child, and the child goes away at the end of the school year.
Grrr.
They wait patiently, and they wait and wait. After all, it's not their child, and the child goes away at the end of the school year.
This is Parental Rage Unit Number One around here.
"There is no need to rush through the curriculum."
Core value as articulated by the powers that be here in Irvingtonland.
It's in trying to define what constitutes scaffolding that the constructivist mischief begins again in earnest.
Indeed, and that's a point I will be making in my presentation. I even have a graphic to go with it. An animated PowerPoint graphic, yet!
It shows a time axis and a stair step type graph, with the desired goal achieve in, say, 15 minutes.
Then there's another stair step type graph, but the intervals between the steps is longer and the time to achieve the goal is about 40 minutes.
The narrative that goes with it is exactly your point. How much guidance one gives is critical, and determines where on the "constructivist spectrum" the teaching is. The other thing that I'll illustrate by hand is that the longer the "run" of the stair step, the more potential there is for students to go off track and not reach the next "rise" of the staircase. This is illustrated by several empirical studies that I cite, in which the author talks about cognitive load theory.
Some of the activities kids are given to do in order to "discover" or reach the goal, results in a three ring circus of ideas in their heads. How are they going to make connections if they don't have the tools to pick out what is most important to solve the problem? CMP is a program that is a prime example of this.
"It's in trying to define what constitutes scaffolding that the constructivist mischief begins again in earnest.
Constructivists deny the possibility of scaffolding by directly instructing or directly telling the child how to bridge the gap between what he knows and what we know he could know next."
That's a very astute observation.
I differ from the constructivists in that I don't believe you should leave a child dangling and frustrated. If prompts don't lead to the desired insights and connections, then you must be more explicit. Being flexible and adapting to the situation is key here.
"The other thing that I'll illustrate by hand is that the longer the "run" of the stair step, the more potential there is for students to go off track and not reach the next "rise" of the staircase."
This is fascinating. Off hand, I would have surmised that a longer run (and consequently a less steep slope) would be beneficial.
This is illustrated by several empirical studies that I cite, in which the author talks about cognitive load theory.
Barry - can I get those references (and/or articles)?
I've been looking for good things to read about cognitive load.
Post a Comment