kitchen table math, the sequel: B.F. Skinner weighs in

Thursday, July 5, 2007

B.F. Skinner weighs in

This is interesting. I had no idea B.F. Skinner had been a foe of ed schools:

Skinner's (1983) classic paper "The Shame of American Education" was originally published in the American Psychologist and later appeared in a collection of Skinner's papers (1987). It was aimed directly at cognitive psychologists. Skinner blamed modern cognitive psychology, in part, for the United States being what the National Commission on Excellence in Education (NCEE, 1983) termed "A Nation at Risk" The NCEE report described the United States as being threatened by "a rising tide of mediocrity." Skinner (1987) also blamed colleges of education as the place where "psychological theories come into the hands of teachers" (p. 120).

[snip]

The failure of colleges of education to teach science and subject- based pedagogy has a long history that cannot be attributed solely or even primarily to cognitive psychology.

[snip]

Evers and Clopton (2003) suggest that progressive ideas in the early 20th century grew from an activist religious piety they termed "pietist millennialism." [I'm not sure what "pietist millennialism" means, but I like the phrase...]



Skinner on discovery

Skinner (1968) made his views of the method of discovery quite clear:

If the student can be taught to learn from the world of things, nothing else will ever have to be taught. This is the method of discovery. It is designed to absolve the teacher from a sense of failure by making instruction unnecessary. The teacher arranges the environment in which discovery is to take place, he suggests lines of inquiry, he keeps the students within bounds. The important thing is that he should tell him nothing.

The human organism does, of course, learn without being taught. It is a good thing that this is so, and it would no doubt be a good thing if more could be learned in that way. Students are naturally interested in what they learn by themselves because they would not learn if they were not, and for the same reason they are more likely to remember what they learn in that way. There are reinforcing elements of surprise and accomplishment in personal discovery which are welcome alternatives to traditional aversive consequences. But discovery is no solution to the problems of education. A culture is no stronger than its capacity to transmit itself....It is quite impossible for the student to discover for himself any substantial part of the wisdom of his culture, and no philosophy of education really proposes that he should. Great thinkers build upon the past, they do not waste time in rediscovering it. It is dangerous to suggest to the student that it is beneath his dignity to learn what others already know, that there is something ignoble (and even destructive of rational powers) in memorizing facts, codes, formulae, or passages from literary works and that to be admired he must think in original ways. It is equally dangerous to forgo teaching important facts and principles in order to give the student a chance to discover them for himself. Only a teacher who is unaware of his effects on his students can believe that children actually discover mathematics, that (as one teacher has written) 'in group discussion they can and do figure out all the relationships, facts, and procedures, that comprise a full program in math' (p. 110).



instructivists!

Skinner pointed out that each of the reform proposals that were being made in the period immediately preceding his paper had a curious omission: namely how teaching could be improved. He described it as a "conspiracy of silence." Skinner suggested that pedagogy had become a "dirty word." Soon after Skinner's paper was published, this silence would be broken and pedagogy would come to the forefront. From the mid 1980's until the present, there has been an open battle between the progressives and the instructivists.

[snip]

During the 1990s the United States underwent an unprecedented curricular "reform" of the public schools. By 1990, the ideological legacy of Kilpatrick, Rugg and Dewey controlled virtually all colleges of education and their respective teacher organizations. The NCTM and the National Council of Teachers of English developed standards reflecting progressive values and pedagogy. These curriculum standards were then adopted by state after state as the frameworks for reading and math. The end result was the standardization of ineffective practices leading to inadequately trained teachers and low-achieving students in basic academic domains (Rumph, Ninness, & McCuller, 2001).


"foundational constituents and complex composites"

Teachers are asked not to teach but to facilitate learning. The teacher is not to tell or show the students but to allow them to discover their own individual knowledge. Paradoxically, it is permissible for an untrained peer to show and tell. The knowledge gained by students is said to be different for each student. Independent reality separate from the person's own knowledge is denied. Progressive pedagogy does not analyze subject matter into foundational constituents and more complex composites, nor does it sequence material in such a way that constituents are taught before composites. Intentionally, the progressives use top down teaching, in which the sequences are inverted such that the more complex skill is introduced first and the foundational skills for it are assumed to be acquired in the context of the more complex task. Slavin (2003) describes top-down teaching this way: "Top-down means that students begin with complex problems to solve and then work out or discover (with the teacher's guidance) the basic skills required" (p. 259). It is not that progressive ideas can never be put to good use; they can (Johnson & Street, 2004). However, using indirect pedagogy to establish foundational constituent skills is simply ineffective and inefficient. Inevitable difficulties will occur in obtaining the skill at all, and in the absence of practice, established skills remain fragile. Weakly established skills are subject to forgetting, hinder the acquisition of composite skills of which they are a component and are less likely to combine with other skills through contingency adduction (Johnson & Layng, 1992).* Behavior analysts Layng, Twyman, and Stikeleather (2004) have developed methods to engineer discovery after directly training constituent skills and using precisely designed instructional sequences. Designed instructional sequences are not a component of contemporary or historical progressive education pedagogy but are a component of most effective pedagogies.

source:
the Shame of American Education redux
(pdf file)
By Rumph, Robin; Ninness, Chris; McCuller, Glen; Holland, James; et al
Author note: Portions of this paper were presented at the 31st annual convention of the Association for Behavior Analysis, Chicago, May, 2005. We gratefully acknowledge Angela Ford for contributions in developing this manuscript. Correspondence concerning this article should be directed to Robin Rumph, School & Behavioral Psychology Program, PO Box 13019 SFA Station, Stephen F. Austin State University, Nacogdoches, TX, 75962
Chris Ninness home page & publications

Robin Rumph and Chris Ninness are professors at Stephen F. Austin State University School & Behavioral Psychology.



spaced repetition: top-down teaching

"Top-down means that students begin with complex problems to solve and then work out or discover (with the teacher's guidance) the basic skills required."

Slavin, R. (2003). Educational psychology: Theory and practice (7th ed.) Boston,MA: Allyn and Bacon.


in a nutshell: behaviorist take on constructivism

  • teachers are facilitators
  • peers, but not teachers, may "show and tell"
  • each student's knowledge is different
  • "independent reality separate from the person's own knowledge is denied"
  • subjects are intentionally taught "top down"
  • "top down" means subject matter is not analyzed into foundational constituents and more complex components
  • material is not sequenced so that foundational constituents are taught before more complex components
  • Robert Slavin: "Top-down means that students begin with complex problems to solve and then work out or discover (with the teacher's guidance) the basic skills required."
  • top-down teaching is "ineffective and inefficient"
  • problems acquiring the skill will inevitably ensue
  • without practice "established skills remain fragile"
  • worse yet: "Weakly established skills are subject to forgetting, hinder the acquisition of composite skills of which they are a component and are less likely to combine with other skills through contingency adduction." [ Johnson, K. R. & Lanyng, T. V. (1992) Breaking the structuralist barrier: Literacy and numeracy with fluency. American Psychologist, 47, 1475-1490.]
  • it is possible to "engineer discovery after directly training constituent skills and using precisely designed instructional sequences" [Layng, J., Twyman, J., & Stikeleather, G. (2004). Engineering discovery learning: The contingency adduction of some precursors of textual responding in a beginning program. Analysis of Verbal Behavior, 20, 99-110.] - but constructivist pedagogy does not do this
  • "Designed instructional sequences are not a component of contemporary or historical progressive education pedagogy but are a component of most effective pedagogies."

* "Contingency adduction occurs when multiple repertoires or components combine with little, if any, instruction (Andronis, Goldiamond & Layng, 1983; Johnson & Layng, 1996; Binder, 1996). "The problem of skill generalisation" (introduction to an unpublished dissertation, I think)


wholes, not parts: Martin Brooks and The Constructivist Classroom
whole math

12 comments:

Anonymous said...

My quick guess of "pietist millenialism" would be that it is related to the post-millenialist belief of the end times (as opposed to pre-millienialists - think "Left Behind" - and amillenialists) that was popular in the late 19th and early 20th centuries. Basically it is the belief that Christ's second coming would be after the millenium, and involves the optimistic belief that the forces of Satan will be gradually defeated by the expandion of the Kingdom of God throughout history. This went hand in hand with the general belief of the time that progress was innately good and that the eventual perfection of the human race was inevitable.

Answers.com mentions a subdivision of postmillenialists somestimes called "Pietistic postmillenialists" that believed in a bottom-up approach for bringing about the millenium - i.e. through people's hearts and minds. That sounds like progressives to me.

-forty-two

Anonymous said...

Oh yeah, there aren't very many postmillenialists around any more - WWI and WWII did a number on the "progress = good" belief, as well as the belief that humanity is capable of perfecting itself.

-forty-two

Tracy W said...

"Top-down means that students begin with complex problems to solve and then work out or discover (with the teacher's guidance) the basic skills required."

How many people who argue for this would agree to be treated by a doctor who was being trained this way?

VickyS said...

What a great post, Catherine. Thanks.

SteveH said...

"Top-down means that students begin with complex problems to solve and then work out or discover (with the teacher's guidance) the basic skills required."


It never happens, unless you redefine what basic skills are required.

Catherine Johnson said...

How many people who argue for this would agree to be treated by a doctor who was being trained this way?

aack! aack!

Turns out there are medical schools that DO teach this way.

There's a whole literature on the problems of professional training....

I think the "case method," which is used in all business schools, gets routinely criticized for relying on this kind of instruction.

Catherine Johnson said...

It never happens, unless you redefine what basic skills are required.

I agree.

I know I've quoted this before. "M.D.," the revered (and retired) writing instructor here in Irvington, told me that if he were starting his career today he would teach grammar directly, instead of embedding it in writing assignments as he was repeatedly told to do. (I got the sense that he was referring to ed schools & professional development workshops, not Irvington administrators per se when he referred to the standing injunction against direct instruction in grammar, btw.)

Catherine Johnson said...

I need to know more about this idea of "generative instruction."

If these people are doing what they say they're doing, they've discovered the royal road to geometry.

I'm certain there is a "royal road," or at least a shorter road than the spiralling road we're on now.

Since I have to do so much reteaching of math here at home, I need the fastest, most efficient way to do it.

Catherine Johnson said...

Question: what is the shortest distance between two points?

Answer: not a spiral

Instructivist said...

["Top-down means that students begin with complex problems to solve and then work out or discover (with the teacher's guidance) the basic skills required."]

SteveH has been talking a lot about "top-down".

I am wondering if he is using the term in the same sense described above?

SteveH said...

"I am wondering if he is using the term in the same sense described above?"

I think I am, but one never knows. Ed school definitions are so fluid. It means that mastery of content and skills are never attacked directly, only as a by-product of other learning.

The is the biggest problem with Everyday Math. There is no initial mastery of the material (except for a few kids). They move right along to new material. This is perhaps better described as distributed mastery. Like top-down learning, mastery of basic skills never gets done properly for many kids.

I have the "new improved" edition of sixth grade Everyday Math and I am amazed at how this jumps out at me. They might have a lesson on some subject that takes up 3 or 4 pages. Often, one or two of the pages are "math boxes" that have little or nothing to do with the subject of that lesson. They are simply review problems of material that should have been mastered in previous years. This is not in-context review of skills. This is just practice that should have been finished long ago. I've been meaning to give some examples and show how different it is from Singapore Math. It appears that 40 percent of the material in Everyday Math is review work. This is NOT distributed practice after mastery. This is distributed mastery, spiraling mastery, or perhaps even top-down mastery. The problem with EM is that there are so many review pages that it's almost impossible to get through all of the units.

VickyS said...

EM "math boxes"--RANDOM! They are fillers requiring absolutely no teaching effort.

Here's what the official EM website says about math boxes:

Math Boxes, originally developed by Everyday Mathematics teacher Ellen Dairyko, are an excellent way to review material on a regular basis.

In Everyday Mathematics, Math Boxes are one of the main components of review and skills maintenance. Once this routine has been introduced, almost every lesson includes a Math Boxes page in the Math Journal as part of the Ongoing Learning and Practice section.

Math Boxes problems are not intended to reinforce the content of the lesson in which they appear. Rather, they provide continuous distributed practice of all skills and concepts in the program. The Math Boxes page does not need to be completed on the same day as the lesson, but it should not be skipped (emphasis added).

Math Boxes are designed as independent activities. Expect that your guidance will be needed, especially at the beginning of the school year when some problems review skills from prior years. If children struggle with a problem set, it is not necessary to create a lesson to develop these skills. You can modify or skip problems that you know are not review for your children. Lesson activities revisit skills throughout the year. Math Boxes also provide useful assessment information on review skills.


Aaack.

But if you really want to torture yourself, look at the student projects in the official Museum of Student Work.

Steve, check out the 5th grade projects--million dollar project, and the very pretty tessellations, and the persuasive essays from the students begging the publisher to keep the factor captor game in the latest edition (do you suppose the kids were allowed to voice a contrary opinion?).

Vicky