kitchen table math, the sequel: cats and dogs living together

Monday, August 6, 2007

cats and dogs living together



ISBN 1-881317-15-3



On its In-Depth page, the Morningside Academy, in Seattle, whose students "typically score in the first and second quartiles on standardized achievement tests in reading, language and mathematics," makes parents this offer:

Morningside Academy offers a money-back guarantee for progressing 2 years in 1 in the skill of greatest deficit. In twenty-five years, Morningside Academy has returned less than one percent of school-year tuition.




from Chapter 6: Comprehension, Critical Thinking, and Self-Regulation

Morningside has wrestled with the problem of guaranteeing that skills taught in isolation truly become an integral part of the everyday activity of the learner. Two methods that we are evolving are designed to bridge typical behavioral skill instruction and useful, real-world application in the spirit of progressive education and John Dewey. When we discuss our procedures with developmental psychologists, constructivist educators, and others outside of the field of applied behavior analysis, we have found them receptive. This is in part a response to our respect for many of their philosophies, methods, and materials. Many of these colleagues maintain activite dialogue with us in our joint effort to find and develop technologies of teaching from basic skills to inquiry and project-based learning.


constructivist behaviorists!

something new under the sun

Here's what they have to say about critical thinking:

Morningside directly instructs and monitors improvement in strategic thinking, reasoning, and self-monitoring skills. Strategic thinking is the glue that allows students to employ component skills and strategies in productive problem solving.... Morningside's instructional and practice strategies build tool and component skills that are needed to solve problems. In addition, most of our students need direct and explicit instruction in "process" or "integrative" repertoires--methods that help them recruit relevant knowledge and skills to solve a particular problem. At Morningside we have found that these strategic thinking skills, characteristic of everyday intellectual activity, are not automatic by-products of learning tool and component skills.

Does this contradict the notion that teaching to fluency, as opposed to mastery, produces contingency adduction? (And see here.)

Are the authors saying that Morningside students have more problems generalizing knowledge to new contexts than students who are doing well in the public schools?

Or are they saying that fluency doesn't increase generalization after all?

I'm getting the feeling that no one really knows how, exactly, critical thinking, problem-solving, and knowledge transfer emerge. As best I can tell, the most that is known is that they don't emerge before mastery of component skills and concepts within a particular domain of knowledge.

More from the book:

There are a number of reasons why traditional efforts to promote creative thinking and problem solving have not been wholly effective. First, watching someone else solve a problem does not reliably teach the process. Second, in routine practice, problem solving behavior is private behavior that other learners can't observe. Third, cooperative problem solving often reinforces already-existing problem solving repertoires of some students in the group, but doesn't enhance the skills in others, even though everyone may come away from the group believing they have "solved the problem."

[snip]

At Morningside, we view the failure to self-monitor and reason during problem solving as a failure of instruction rather than as a failure of the learner. This perspective has provided a challenge to develop instructional strategies that turn learners into productive thinkers and problem solvers.


A note: for those of you who aren't familiar with behaviorism, this is a -- or even the -- core tenet of the field. If an instructional approach isn't working, the problem lies in the instruction, not the student. Or, rather, the problem lies in the contingencies; that might be the proper way to put it (don't know). I'm not sure you could be a behaviorist without subscribing to this principle.

This principle -- it's the teaching, not the student -- led Irene Pepperberg to her breakthrough with Alex the parrot (chapter excerpt), by the way.

Back to Morningside:

Thinking Aloud Problem Solving
To develop these strategies and to provide students with a set of self-monitoring, reasoning, and problem solving strategies, Morningside turned to an approach developed by Arthur Whimbey and Jack Lockhead in the 1970s...They developed Thining Aloud Problem Solving (TAPS) to improve analytical reasoning skills of college students. Perhaps the most impressive evidence of its effectiveness comes from its use at Xavier University in a four-week pre-college summer program for entering students. The program, Stress On Analytical Reasoning (SOAR), was replicated over several summers at this perdominantly African-American college and produced stunning results.... Participants gained 2.5 grade levels on the Nelson-Denny Reading Test and an average of 120 points on the Scholastic Achievement Test. (p. 122)

This assertion flatly contradicts the conclusion of cognitive science that critical thinking and problem solving cannot be taught directly, at least not separately from extensive teaching of content. At least, I think it does; I don't know what kind of domain knowledge was involved in this program.

Interesting.


the cog-sci position

The Mind's Journey from Novice to Expert by John T. Bruer

A few of these programs, such as the Productive Thinking Program (Covington 1985) and Instrumental Enrichment (Feuerstein et al. 1985), have undergone extensive evaluation. The evaluations consistently report that students improve on problems like those contained in the course materials but show only limited improvement on novel problems or problems unlike those in the materials (Mansfield et al. 1978; Savell et al. 1986). The programs provide extensive practice on the specific kinds of problems that their designers want children to master. Children do improve on those problems, but this is different from developing general cognitive skills. After reviewing the effectiveness of several thinking-skills programs, one group of psychologists concluded that "there is no strong evidence that students in any of these thinking-skills programs improved in tasks that were dissimilar to those already explicitly practiced" (Bransford et al. 1985, p. 202). Students in the programs don't become more intelligent generally; the general problem-solving and thinking skills they learn do not transfer to novel problems. Rather, the programs help students become experts in the domain of puzzle problems.


Critical Thinking: Why Is It So Hard to Teach? (pdf file)
by Daniel Willingham

After more than 20 years of lamentation, exhortation, and little improvement, maybe it’s time to ask a fundamental question: Can critical thinking actually
be taught? Decades of cognitive research point to a disappointing answer: not really. People who have sought to teach critical thinking have assumed that it is a skill, like riding a bicycle, and that, like other skills, once you learn it, you can apply it in any situation. Research from cognitive science shows that thinking is not that sort of skill. The processes of thinking are intertwined with the content of thought (that is, domain knowledge). Thus, if you remind a student to “look at an issue from
multiple perspectives” often enough, he will learn that he ought to do so, but if he doesn’t know much about an issue, he can’t think about it from multiple perspectives. You can teach students maxims about how they ought to think, but without background knowledge and practice, they probably will not be able to implement the advice they memorize. Just as it makes no sense to try to teach factual content without giving students opportunities to practice using it, it also makes no sense to try to teach critical thinking devoid of factual content.


I would sure like some help on this issue, seeing as how I am living in failure to transfer land. For the time being I'm going to carry on assuming fluency will help -- fluency and lots of practice with word problems:

Give me a problem which you think is not by type, and I shall invent ten similar problems which will put it into a type. In fact, I often have to do this when I teach: first I solve a problem at the board, then I give a similar problem for all to solve in class, then I give a similar problem as a homework, then I give a similar problem on a test. All these stages (often more) are necessary, otherwise many students will not grasp the method.
Between Childhood and Mathematics: Word Problems in Mathematical Education (pdf file)
by Andrei Toom


Between Childhood and Mathematics: Word Problems in Mathematical Education (pdf file)
Word Problems in Russian Mathematical Education (pdf file)
How I Teach Word Problems (pdf file)

The Executive Brain
Meet Alex

19 comments:

Karen A said...

Several years ago, I taught a course for college freshmen that had, as one of its objectives, an introduction to critical thinking. (I taught the course for three years; it no longer exists in its present form, however.)

I used the text, "Asking the Right Questions: A Guide to Critical Thinking" by M. Neil Browne and Stuart M. Keeley.

Each section had a theme, chosen by the individual professor, and the idea was to explore the elements of critical thinking, through the use of content.

Personally, I loved teaching the class. For one thing, my own critical thinking skills and horizons were expanded. In law school, we are taught that we have to know our opponent's case and arguments as well as we know our own. I sometimes refer to this as thorough thinking as well.

I suppose, though, that this begs the question as to whether such skills can be taught as a process, and if so, to what extent. My personal experience was that one doesn't learn or acquire the skills in a vacuum; there has to be a content of some sort to use for that purpose.

Karen A said...

Many young people today have very strong opinions about all sorts of issues. One of my objectives was to teach them to learn the difference between fact and opinion.

Another objective that I had was to talk about the role of emotions and "personal baggage." Our emotions are what tend to get us interested; however, we have to learn to set aside our emotions at times in order to be able to determine the facts. That is, I would talk to them about the important role that emotions can play, but how emotions can also cloud our judgment.

Karen A said...

I also asked the students to evaluate short passages of material. For example, perhaps an op ed piece or a syndicated columnist. I would ask them to determine what the author's conclusion was; that is, what was the major point that the author was trying to convey, and what were their reasons in support of their conclusion.

Oh, I also used letters to the editor from our local paper, some of which were well written, and others that weren't.

We would also look for the possibility of bias. An op ed piece in the Wall Street Journal may have a different slant on an issue than the New York Times, for example. Likewise, columinists like Cal Thomas and Molly Ivins had a bias, so we talked about that as well.

Sometimes, it was hard for the students to discern the author's conclusion; sometimes that was because the article itself may not have been well written. This served the dual purpose of emphasizing how important it is to be clear in one's own writing, which often requires a great deal of thought.

Karen A said...

I realize that my above comments are rather cursory in nature. However, the point I was trying to make (ah, the conclusion!) is that I do think that there are elements of "critical" thinking that can be taught as a process. Or, perhaps another way of saying that is that I think that there are habits of thought that can be learned.

Lawyers sometimes drive themselves (and others!) crazy by always asking, "Why?" or "What if?" or "If I do this, what happens next?" As a quick example, when drafting estate planning documents, one of our goals was to never have a will or trust without a contingent beneficiary. That is, we never wanted to have a disposition fail and have the property go to the state. This was more of an issue when clients had very few surviving family members. So, we would always ask, "What if all of these people die before you do? To whom would you then wish the property to go? Do you have a charity that you prefer?"

I should note that on the first day of class, I would always be sure to explain that critical thinking for purposes of this class was not the same thing as "criticism." I used that as a starting point in my never-ending quest with them to underscore how important vocabulary is in getting one's point across. (There would always be a group of students who had never heard of the concept of critical thinking; for them, it meant criticism.)

Karen A said...

Yikes! Somebody needs to stop me! (I'm in major procrastination mode--I'm supposed to be writing a paper.)

Anyway, as a preliminary matter, I think an important first step in critical thinking is learning to identify conclusions and the reasons that are given in support thereof. That is, what is it that the writer/speaker wants the audience to believe, and what are the reasons offered in support thereof.

I think doing this is also a very powerful exercise to strenghten one's own writing as well.

Karen A said...

Good lord, here I am again! Anyway, one of the points of learning to ask questions for a writer is that it helps the writer close potential holes, and to answer questions that the reader might have.

Here is where I shamelessly plug Animals in Translation (the book that Catherine co-authored with Temple Grandin) in this respect. I thought the book did a marvelous job of anticipating the questions that the reader would have, and then answering those questions.

Another feature that I liked (and again, I think this is an element of critical thinking/writing) is that the authors avoided the absolute. Instead, general principles (about skittish horses, for example) were enunciated, but the possibility of exceptions to those general principles were also noted and explained. I thought this greatly added to the credibiity of the argument, as it were.

The other feature, and I suppose that this is what helped make the book a bestseller, is that difficult (and fascinating) concepts from a variety of disciplines were explained in the context of stories and examples that the nonexpert reader could follow. That is, it was user-friendly in that regard.

Catherine Johnson said...

Many young people today have very strong opinions about all sorts of issues. One of my objectives was to teach them to learn the difference between fact and opinion.

That is a MAJOR goal.

I've been backing off from the teaching-via-op-eddery approach for this reason.

People seem to try to teach critical thinking skills by having kids read and write mini-op eds.

I understand exactly why they do this; it's one of the few ways to demonstrate critical thinking without much background knowledge.

But I think it reinforces the idea that writing is about opinions, not evidence.

Catherine Johnson said...

I'm also backing away from the "writing is argument" concept (this is a biggie for Ed - papers have to have arguments).

I'm going back to the idea of a "theme."

What a terrific word, theme.

Catherine Johnson said...

Lawyers sometimes drive themselves (and others!) crazy by always asking, "Why?" or "What if?" or "If I do this, what happens next?"

Lawyers as a group, I think, are phenomenally good writers.

Catherine Johnson said...

I'm in major procrastination mode--I'm supposed to be writing a paper.

SNORT

le radical galoisien said...

"But I think it reinforces the idea that writing is about opinions, not evidence."

Which is why I am so satisfied with the AP Language and Comp course, which is heavy on rhetoric.

Of course, it could also be that I had a great teacher, so I don't know. Personally, I think most of my peers are capable of judging sources and authority. The internet was a medium that greatly shaped my writing skills, because I had to use sources to my own end (to convince other people on my own terms) and not merely fulfill an assignment.

In a writing assignment, the top requirement should be, "make a convincing argument." That should be the most important rubric, not, "I want this to be so many words long."

"Lawyers as a group, I think, are phenomenally good writers."

But not necessarily good spellers! I think I mentioned this in another post, but my retired lawyer of a teacher is dyslexic.


"I'm also backing away from the "writing is argument" concept (this is a biggie for Ed - papers have to have arguments)."


But everything is an argument! Not everything is necessarily sharp argument though. The classic essay format teachers ask you to write is what I call a "brute force argument". On the AP Lang and Comp exam, most people write in essay format for the argument question, but those who do it in narrative do it poignantly.

le radical galoisien said...

And as a student, I have never really grasped what this "critical thinking" is all about.

Really, I get peeved at textbooks which list "CRITICAL THINKING" questions that are tedious to answer but do not actually involve anything enlightening.

And when they talked about the "CRITICAL THINKING" problems in the PSLE syllabus, I didn't notice any real difference.

And it is a sad truth that you can always study for any type of question, which is one of the flaws of testing solely by exam. For example, when they introduced PSLE HEURISTICS (complete with allcaps) with hell and fury some years ago, enough for my form teacher to promptly make us do remedials and buy us extra assessmentbooks concerning PSLE HEURISTICS than among other things involved CRITICAL THINKING skills, we did some relatively new types of problems that for example involved questions like:

What is the sum of 8 + 11 + 13 + 15 + .... 103?

and variations thereof, got pretty old quickly. (12 + 15 + 19 ... ; 104 - 103 + 101 - 98 + 94 - 89 ..., etc.)


Personally I thought the old PSLE problems exercised a lot of thinking already.

Of course, it introduced us to series, which comes in pretty handy when you do Taylors.

Catherine Johnson said...

But everything is an argument!

I know.

But I'm tired of this now; I've been hearing it (and, on occasion, saying it) for possibly 20 years.

Every ten years or so I decide that all of life can be explained by "X."

In my 20s I thought all of life could be explained by "power."

Then, maybe in my 30s, I decided all of life could be explained by "status."

Then somewhere in there I decided all of life was "selling" (which is the same idea as "all of writing is argument").

The idea that "all writing is argument" (there is even a textbook by this name) comes from a particular time and politics (pretention alert)....and I'm just tired of it.

Sure, you can call a descriptive essay an argument.

But I don't want to!

Catherine Johnson said...

Really, I get peeved at textbooks which list "CRITICAL THINKING" questions that are tedious to answer but do not actually involve anything enlightening.

I'm just grateful I've only had to deal with this as a parent.

I think.

Catherine Johnson said...

otoh, I never had the privilege of being introduced to series....

Catherine Johnson said...

You might like David Mulroy's War on Grammar.

He makes an interesting argument (!) about over-emphasis on argument.

He says the same thing happened in Medieval times.

Karen A said...

"But everything is an argument!"

Several years ago, while in the midst of teaching the above-described class, I had a student stop by to ask for help with a letter he was writing to a prospective employer.

Well, I seized the day! What a perfect opportunity (at least in my poor feeble mind) to convince the young man that the skills we were learning in class actually had a real world application, namely that of convincing this employer to give him an opportunity for an internship.

My point to him was that he was trying to convince this person that he was worthy of an internship, or at the very least, an interview.

Karen A said...

The textbook that I used defined an argument as follows:

argument = conclusion + reason(s)

Barry Garelick said...

I know on the Hill everything is an argument including what day of the week it is.