From: Clyde Greeno @ MALEI Sent: Sunday, March 18, 2012 12:06 PM To: Jack Rotman Subject: Re: What's the Meaning of 'Direct Instruction'? > constructivism
Jack's brief comments deserve several clarifications ... which, unfortunately, cannot be as brief.
Re: " The Engelman 'definition' ... " One of the major flaws of collegiate instruction in STEM-fields is its failure to educate its graduates in the nature of technical definitions ... as opposed to how dictionaries are used with respect to commonplace discourse. In essence, dictionaries result from statistical inferences ... about what meanings of a word are the commonly accepted. Those give the best available approximations of what a word "really means" within the established culture. But a scientific "definition" of "work" ... as the product of force and motion .. is not at all an attempt to identify the "real meaning" of the term, "work." Rather, it identifies the phenomena of a-force-being-applied-throughout-a-distance ... and conveniently labels it by the shorter term, "work." That distinction between "commonplace" and "technical " kinds of "definitions" now must be applied to DI.
In scientific perspective, " The Engelman 'definition' ... " must not be construed as describing what "direct instruction" is ... but simply as his wording for what is more accurately called "Engelmann Instruction." Its central essence is "Faultless Communication" : http://psych.athabascau.ca/html/387/OpenModules/Engelmann/glossary.shtml#faultless . That brings us back to "direct instruction" as instruction done by direct transmission of instructor-composed messages, for learner-interpretation into actually-received messages ... with all kinds of communications-channel constraints interfering with the reliability of the process.
No thoughtful educators would ever regard direct communication "... as an 'automatic bad thing' ...." Neither would they fail to recognize the extreme difficulty and low probability of achieving "faultless communication" though reliance on formal languages in which the receivers are not already very fluent.
"There are accepted research studies (with associated theory) on types of direct instruction ..." Good to know! It is very important for the profession to compile a list of such studies ... if only for producing a conceptual taxonomy of various "types of direct instruction ." But all kinds that so-qualify would seem (like Engelmann's) to fall within the generalizing arena of *instruction via direct communications.* I am as dubious about whomever has "accepted" whatever "research" pertains to each of those types ... as I am about any "associated theory" for each such type. That seemingly glib claim might very well be absolutely true, and probably is at least partially so. Perhaps it is time to activate a wikisite that is devoted exclusively to "The Nature, Types, Pros, and Cons of Direct-communications Instruction."
The huge size and inconclusiveness of the PFT study is significant far more for what it says about government spending than for its statistical importance to educators. Engelmann was a pre-school teacher, and the Engelmann version of DI was used only with impoverished children in the lower grades. Because very young children are (developmentally) not miniature adults (and learn in very non-adult ways), PFT certainly has no bearing on non-primary levels of education. The results seem to imply only that Engelmann Instruction works well for training impoverished, infantile minds to jump through simplistic hoops (which is probably why it failed its intended purpose of helping to win "the war on poverty"). But for purposes of guiding adolescents and adults to rationally resolve complex phenomena into personal common sense ... as needed for response-able managerial thinking ... Engelmann's "faultless communication" requires much greater linguistic expertise not only within the instructors, but also within the students.
" The theoretical basis is stronger for direct instruction .... " I do wonder about just what "theoretical basis" warrants that allusion. I look forward to learning more about it. To the best of my knowledge, the scientific theoretical basis for instruction-via-direct-communications is a blend of cybernetics, linguistics, convergent (state-transition) probability-matrices and communications theory. But I do not yet know of any works that meld those ores into a metallic basis for instructional practices. Together, however, they do disclose a vast spectrum of causes for why person-to-person "flawless communication" is nearly impossible to achieve. Nonetheless, serious instructological attention to those various theoretical footings can shed much light on how to improve the effectiveness of DI.
" ... than it is for the 'constructivist' view of learning. ("Constructivism" is not a theory of learning, since it does not generate hypotheses that can be tested; in other words, constructivism lacks the capacity for 'failing results', a key component of any productive theory.)"
All depends on what understanding one uses for the term, "constructivism." In its most naïve meanings ... which seemingly are what are most commonly used by lay persons and by most educators ... the quoted assertion probably is close to the truth. In those meanings, "constructivistic" instruction is a mode of teacher performance, rather than an instructional application of learning-theory. It typically reduces to some kind of "guided discovery" ... in which the instructing "guide" leads the students along a succession of landmarks which the students hopefully will achieve ... while the guide is oblivious to what is happening between students' ears. One extreme of that kind is where students "discover" some kind of performance-pattern that the teacher wants students to emulate. When that is what is meant by "constructivism", the quoted assertion is quite realistic.
However, the same assertion is totally absurd ... when the term, "constructivism", is scientifically used with the following meaning ... which is a formulation of what most of its knowledgeable proponents appear to mean. All humans develop functional personal intelligence partly by internally generating information and assembling it into dynamically evolving mental structures that are held and used as (in essence) personal "theories" about all kinds of things. Although we also use other, more animalistic modes of learning, we all learn some things *theoristically* ... by "theorizing." [That is how infants learn a language.]
Humans are distinguished by their natural, inborn capacity for theoristic learning (which is not totally peculiar to humans). Without relying on theoristic learning, no human can manage to survive. It is a far more humanly natural kind of learning than is learning via communicates from others. Our "theories" typically are very rough, rarely are formulated into languages, and often function subconsciously. Nonetheless, we depend on our personal "theories" as our "knowledge" ... or as our best approximations to it. That is what psychoanalytic therapy is all about, and instruction often is done with strong, intuitive regard for theoristic learning.
Within the human mind, personal theories *grow* ... by thinking with and about what we already "know" ... often by accepting, assimilating, and accommodating information newly accrued from outside sources. Such theoristic learning is done by continuing our internal construction of personal theories. In that meaning, "constructivism" is very much a theory of *theoristic* learning. The scientific theory of theoristic learning manifests in several areas ... cognition theory, psycho-linguistics, and psychiatry, for examples.
Theoristic learning also is how mankind's knowledge, cultures, and technologies have evolved. ... and mankind's long history of evolving through theorizing stands as undeniable proof of its validity and usefulness. [For those concerned about "... hypotheses that can be tested [and/or] the capacity for 'failing results' ..." clinical research in the instructional guidance of theoristic learning routinely suffices.]
To perceive "constructivism" merely as a mode of instruction is to disregard its scientific foundations. The scientific psychomathematical theory of personal mathematical comprehension is based on the psychology of theoristic learning of mathematical concepts, facts, and processes ... as done by infants, research mathematicians, and everyone in between. In that context, "constructivistic instruction" so-functions by guiding learners to internally acquire new knowledge by personal theorizing ... thereby internally developing the new, from what they already knew ... by using personal senses and reasoning powers. Such learning commonly happens through explorations with physical objects or media. It often happens also by interpreting communicates.
SURPRISE!!! The (constructivistic) instructional guidance of theoristic learning does not at all conflict with instruction via direct communications! The supposed conflict is a straw man. Instructors who can make safe presumptions about what mathematical theories already are owned by their students ... and about the shared communications systems ... might very effectively use direct communications to guide their students to develop their own mathematical theories as guided by the instructor ... "constructivistic direct instruction", if you wish ... or "direct constructivistic instruction." Many famous mathematicians have been quite talented in that area.
On the other hand, the instructional guidance of theoristic learning also can be done, indirectly, by leading the learner to internally develop instructor-targeted information without the instructor ever transmitting messages that express that information. That kind of coaching others to "learn from experience" goes back to the cave men. In contrast, instruction can be done via direct communications (Khan-wise), without guiding the learners to achieve the needed additions to their personal theories. That process has long (and disastrously) permeated curricular instruction in mathematics.
So it is seen that the essence of "the math war" is not really about "direct Vs indirect" instruction. It actually is about whether or not students should achieve theoristic mathematical comprehension as personal common sense. When that can be adequately accomplished through direct communications, that is the more expedient mode. But when that mode is unreliable ... or when a stronger kind of "adequacy" is sought ... the shortcomings of direct communications can badly curtail instructional productivity.
The underlying learning theory boils down to this. The learning of mathematics as a fragmentary toolbox of concepts, facts, and skills is far less beneficial (lasting, useful, gratifying, reliable, empowering, etc.) than is learning those same elements as integrated components within cohesive mathematical theories that fully are mathematically commonsensible to the learners, themselves. For students who are not already fluent in the communicative languages, their theoristic growth is far less likely to adequately respond to direct communications than to instructor-guided, hands-on, experiential, exploratory, laboratory-learning, activities. Which mode is "better" depends on ... "for whom" and "for what." It is almost certain that the PFT data was all about children's' performances on traditionally oriented scholastic tests ... rather than about the theoristic growth of their functional personal mathematical intelligence.
"Most modern instructors in community college mathematics have evolved a direct instruction approach with other methodologies used based on need. We should not confuse 'direct instruction' with 'lecture'; there is a huge difference. Few of us ... myself included ... are gifted enough to use a true lecture as a learning method."
So, go with whatever works ... for making school/college mathematics fully commonsensible to all serious students. Teachers who can do so via direct communications of whatever mathematics they know (by lectures, handouts, A/Vs, etc.) will find it far more expedient to use direct communications. [Of course, in that mode of instruction, the learning cannot go far beyond what the teacher knows ... so the teachers had better know far more than whatever they teach.]
However, nothing can be mathematically worse for students than to have their scholastic success (scores, grades, credits, GPA's, financial aid, preparation for other courses, degrees, future opportunities, academic self-images, etc.) depend on how well they can memorize "definitions", facts, and process that make no common sense to them. It ruins their potentials, wastes their time and our money (and theirs), and belies the notion of "college education." Unfortunately, that presently is the "mainstream" of American core "education" in "mathematics" ... grade-4 through calculus.
The popular textbooks badly fail to impart theoristic comprehension of the topics they attend. ... and collegiate success-statistics suggest that most instructors don't do much better than the books that they use. When teachers recognize that they are expediently relying on direct communications ... without actually guiding students to internally digest those topics into personal mathematical theories that are common to the students, themselves ... professional responsibility dictates that they change their ways (their placement tests, books, media, testing/grading systems, curricula, program structures, institutional policies, instructional modes, ...). If the New Life movement makes collegiate mathematics more commonsensible to the nation's remedial students, it will become a great step forward. If it merely causes a re-forming the traditional, anti-theoristic curriculum, its evolution will become a sham.
From: Jack Rotman Sent: Saturday, March 17, 2012 2:21 PM To: Guy Brandenburg ; Alain Schremmer Cc: wmackey ; Clyde Greeno @ MALEI ; email@example.com ; Richard Hake Subject: Re: What's the Meaning of 'Direct Instruction'?
Not that many other people are reading this thread (besides the few of us posting) ... but I will add a different perspective. Most of the literature dealing with research on direct instruction lacks a consistent definition (a problem shared with most other models as well). The Engelman 'definition' has one of the longer pedigrees, going back to the early 1970's. For those who look at DI (direct instruction) as an 'automatic bad thing', I would point you to the results of the largest educational research project every conducted in this country -- Project Follow Through (start at http://darkwing.uoregon.edu/~adiep/ft/grossen.htm to get some information).
There are accepted research studies (with associated theory) on types of direct instruction, more broadly defined as "instructor led classroom processes". The theoretical basis is stronger for direct instruction than it is for the 'constructivist' view of learning. ("Constructivism" is not a theory of learning, since it does not generate hypotheses that can be tested; in other words, constructivism lacks the capacity for 'failing results', a key component of any productive theory.)
Most modern instructors in community college mathematics have evolved a direct instruction approach with other methodologies used based on need. We should not confuse 'direct instruction' with 'lecture'; there is a huge difference. Few of us ... myself included ... are gifted enough to use a true lecture as a learning method.
Jack Rotman Professor, Mathematics Department Lansing Community College (517)483-1079 firstname.lastname@example.org www.devmathrevival.net
-----Original Message----- >From Guy Brandenburg <email@example.com> Sent Sat 3/17/2012 1:17 PM To Alain Schremmer <firstname.lastname@example.org> Cc wmackey <email@example.com>; Clyde Greeno @ MALEI <firstname.lastname@example.org>; email@example.com <firstname.lastname@example.org>; Richard Hake <email@example.com> Subject Re: What's the Meaning of 'Direct Instruction'?
On Mar 17, 2012, at 12:51 PM, Alain Schremmer <firstname.lastname@example.org> wrote:
> > On Mar 17, 2012, at 12:21 PM, wmackey wrote: > >> Exactly right! Well said Clyde >> >> wayne >> > Exactly right > > --schremmer >> >> Quoting "Clyde Greeno @ MALEI" <email@example.com>: >> >>> > What's the Meaning of 'Direct Instruction'?Taking the word apart ... >>> > as "in-struct" ... meaning "inducing the internal structuring of >>> > information" ... the phrase "direct instruction" is >>> > self-contradictory. >>> > >>> > In practice, all four perspectives, below, suggest that "direct >>> > instruction" typically refers to *direct communication* of >>> > information ... from transmitters to receivers ... with or without >>> > collateral use of mechanisms for ensuring that the messages so >>> > acquired by the receivers are adequate interpretations of the >>> > messages expressed by the transmitter. >>> > >>> > The national hunger for Khan-type "direct instruction" manifests >>> > popular preference for being told how to gain favor by performing as >>> > directed, rather than for achieving functional personal intelligence. >>> > Our math-education traditions thoroughly train school students for >>> > such subservient stupidity ... which is why so many end up as >>> > math-fearing, math-illiterates who flounder in collegiate remedial >>> > courses ... or as druggies or criminals. >>> > >>> > Cordially, >>> > >>> > Clyde >>> > >>> > >>> > > **************************************************************************** > * To post to the list: email firstname.lastname@example.org * > * To unsubscribe, email the message "unsubscribe mathedcc" to email@example.com * > * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 * > **************************************************************************** **************************************************************************** * To post to the list: email firstname.lastname@example.org * * To unsubscribe, email the message "unsubscribe mathedcc" to email@example.com * * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 * ****************************************************************************