A definition of rigor

[Diviya]

This is from The Heart of the Mind, by Michael Clay Thompson, which is a collection of essays. This is from the essay entitled "Give Me Rigor or Give Me Mortis". My apologies if you have already seen it.

 

"Imagine a vertical continuum of challenge. The challenge at the bottom is zero; every student can do everything asked already, and no new learning or mental effort is required. Much of American education falls into this category; research consistently shows, for example, that bright students can answer eighty percent of final exam math questions before taking the course.

 

The challenge level in the middle of the vertical continuum is minimal. Students already understand most of what is required, and the few details that are new do not provide enough growth to generate excitement. Students come home every day and answer "Nothing" to you-know-what question.

 

Higher on the vertical challenge continuum, we find a level of genuine difficulty. There is some real demand, some interesting complexity, a bit of abstraction, and a dash of depth. Here and there, the minds light up, and begin to read and learn, feeling that at last, their time is not being wasted. Still, no deep growth is required; students do this work with equanimity, feeling that though more interesting, it is well within their ability.

 

Even higher on the continuum, there is a level of stringent, severe difficulty, that makes strong demands of students through advanced levels of reading, abstraction, complexity, and pace, but which nevertheless remains within the realm of familiar terrain. Students here are doing more complex and elaborate varieties of things they have already done. They are learning more, faster, with more mastery and discipline, but no change is required in the way they think of themselves.

 

Above this, high up on the challenge continuum, there is a thin, almost unnoticeable band. It represents a level of rigor so challenging that beyond requiring students to study difficult content, it requires students to reconsider themselves. At this level, a small amount of fear creeps in. Rapid breathing ensues. The thrill factor jumps. Students not only do not know the material at all, they are not sure they are in the right place. They are not in Kansas anymore. Moses-like, they are intellectual strangers in a strange land. To answer the demands of the assignment, they must not only learn what is new, they must be what is new.

 

Master teaching, for gifted children, involves positioning the learning demands right at this seam, forcing students not only to learn, but to molt, to crack off the crusty shells of exoconcepts and get bigger. The unthreatening hard study in the level below is insufficiently rigorous because it builds their knowledge without developing their selves, and the really threatening impossibility in the level above is inappropriate because it will bruise them with failure, but between the difficult and the impossible is the rigorous."

 

My thoughts later...

[Ester Maria]

I have just regained my hope in humanity - for a small fraction of time, I know, but still, wow, I regained it for a whole moment. Thank you. :)

[Guest]

This is tremendously thought-provoking, and he gives wonderful descriptions of the various levels he is categorizing. Thanks for posting it!

 

One of the most interesting aspects, for me, is the explanation that that gifted kids ideally need their learning to be positioned "on this seam" between very demanding but familiar, and completely complex, requiring re-conceiving of the self.

 

There are a lot of gifted kids in the world, but proportionally, they are a small segment of the student population. What level of teaching/learning do all the other kids need? Would they be unable to ever reach levels of thinking which require them to re-imagine themselves? Would they be incapable of "true" rigor, or is that the province of the gifted alone?

 

Another thought I had regarding this same issue comes from an upper division course at the University of California on autobiography in which kids were asked to read, among many other more classic texts, one of Temple Grandin's books. These very intelligent and capable students had tremendous difficulty grappling with a construct of identity so different from their own: "She's so self-centered! She keeps talking about those stupid cattle chutes! This isn't what autobiography is supposed to be like!"

 

The professor then showed the kids a video interview of Temple Grandin and talked at some length about what is known about autism. The kids's world-view, their cultural ways of defining identity, and their beliefs about autobiography, were all truly shaken and challenged in a way I think really fits with what MCT describes.

 

Now consider this: autistic kids, particularly those on the higher end of the spectrum who are very aware that they are different and that their experience of the world is unlike that of most people's, CONSTANTLY deal with precisely this same challenge to their ideas of self, the nature of what constitutes reality, the variability of people's perceptions; and this intersects with the content they learn in school in a number of highly complex ways.

 

So one could argue that extremely intelligent, high-functioning spectrum kids like this are living their entire lives in that state of heightened, blood-pumping anxiety and the overturning of beliefs or understandings that the quote describes as the highest, most difficult, most complex level of rigorous thought. (Maybe that's why they're always so exhausted!)

 

I do not say this to challenge or in any way disagree with the quote, which I really liked. Given the incredibly high numbers of kids on the spectrum in all countries and across all kinds of cultural and social divides, I just found it interesting that the quote describes that highest level of rigor so utterly from the point of view of neurotypical thinkers, and I got to wondering what a description of levels of intellectual rigor would look like if it were written by someone wired very differently -- gifted and on the spectrum is the main example that came into my head because my dd is an Aspie.

[FaithManor]

KarenAnne,

 

I really understand what you are saying. I would also like to posit that at one time, that level of education, the stretching, changing, molting, but not bruising type of education was a standard in American education. My parents in the 50's and very early 60"s describe how much high school studies shaped them, how much they were challenged, how much they grappled with very, very difficult topics, the high standards for their output, and complex levels of challenging/rigorous thought. Now, even by then it was waning into a distant dream, but pockets of schools still had it. My mother practically majored in "home economics" in her high school. What they had to achieve by 12th grade would make most of us seasoned moms, quake in our boots! My dad's practical drafting skills were such that he was able to enter the air force for missile mechanics and engineering without college. That's some serious training!

 

I do also understand what you are saying about neurotypical thinking, but I also think that at one time in this nation, a much greater percentage of people were able to think in highly complex ways. I think complex thinkers stick out more today than before. Modern educational theory, teaching to narrow specs, one size fits all education, lowering standards, behavioral problems in schools, etc. have, I believe, led to an acceptance that most individuals cannot think at these levels and this should be left to those with the "gifted label". My parents and many of their friends would have been considered average in their generation and yet, by today's standard of gifted, they meet or exceed those expectations.

 

As for what do other kids need? Regardless of what level of academic achievement is reached, I think that an excellent/rigorous education is one that does challenge, mold, re-shape, and re-define. For some, they may reach that sooner than others and for some, the work that does that for them may be more or less difficult than it is for others. There probably is not one hard and fast, "here is the line....on the left, not rigorous and on the right, rigorous."

 

That said, I also don't think it is quite as subjective as we'd like to think it is. High school should be demanding, it should stretch the child, it should make their horizons shift, it should require tremendous effort to attain whatever level of achievement that matches the capabilities of our children. We shouldn't underestimate them and it should be hard work. We shouldn't hurt them, but making them a bit tired at the end of the day, well, that's okay.

 

I think the reponse to Temple Grandin's Book is a "case in point". I'm not certain that if a similar book were presented to high schoolers in the 1940's or 50's, the students would have grappled with the content and themes. I truly think they were more challenged in their thinking, again that classical approach. My dad says that what most kids study in 9th and 10th grade today, except for mathematics and sciences which required upper divisional math skills, he was studying in 6th grade. So I have to wonder if modern culture considers logic stage learning as high school level which leaves college to be rhetorical stage learning instead of exploring to greater depths and heights.

 

You know what? I'm not articulating well here and I don't want to offend anyone. I'm struggling to say what I mean and I do understand also what KarenAnne is trying to say. So I will leave this discussion for a while with one final thought.

 

More than anything I value compassion, self-discipline, perseverance, and kindness. There is nothing I have to offer my children in the academic realm that is of any enduring quality if my children do not become positive, contributing citizens of planet earth. I would rather leave the academics behind, if it for some bizarre reason came down to a choice between learning X thoroughly and becoming a lovely human being, and pursue excellence in character development. I can think of no greater catastrophe than my dd, instead of being the compassionate, loving, "I treat all my patients as one of God's beloved creation", merciful, medic/pre-med student she is, becoming a cold-practitioner that saw her patients as nothing more than puzzles to be put back together, equations to be solved. That would feel like an utter failure for me and for her. I am ever so thankful, so blessed, that she turned out the way she did. Wow! Now that was a little off-topic, wasn't it?

 

Hmmmm.....I need to think.

 

Faith

[Hunter]

The thing to remember about some highs chools in the past, is that only a small percentage of students attended these schools. Many, many students spent 10 years completing the 8th grade and then went no further, and many students were attending alternate schools.

 

When the college prep high school scope and sequence was developed it was never intended to be for ALL teenaged students. We now send all of our students to high school, and call the college prep scope and sequence "high school" and then try and figure out how to tweak it for all students. The scope and sequence is innapropriate for a large percentage of teenaged students at it's very core and foundation, and even when tweaked is still a poor fit.

[Guest]

I just lost a long and involved post, which might be a good thing...

 

I understand the quoted bit of the essay to be talking about this: looking at our pre-established understandings, finding ways to complicate, stretch, or challenge them, and coming to new understandings with an even higher degree of awareness or complexity or a different point of view.

 

I think the Temple Grandin is still an excellent example. The kids in the upper division literature class were reading Augustine, St. Teresa, Edward Gibbon, James Boswell, Virginia Woolf -- classics all -- along with a selection of different theoretical definitions of autobiography as a literary genre and philosophical definitions of selfhood. It was difficult stuff and was already stretching their understandings and complicating their notion of a stable self and what autobiography could or should look like.

 

Temple Grandin's book threw them for such a loop because what they realized was that all these various writers and the theorists as well, varied as their works and ideas were, all shared underlying assumptions about the nature of identity which did not and/or could not account for a completely different version as seen through the mind of a person on the spectrum.

 

I know this is very different and the comparison isn't exact, but the analogy that comes to mind nevertheless is an astrophysicist realizing that most of the universe is actually unseen and unseeable, made up of dark matter whose composition he or she cannot identify.

 

Underlying entrenched assumptions, be they intellectual or cultural, are the hardest kinds of things to re-examine and re-evaluate, partly because they are so much like the very air around us, so much taken for granted as universal and factual that we can barely even see them as constructions. The fear that MCT describes, which accompanies the thrill, is a reaction to the fracturing of our certainty about what is known and how we know it.

 

There are a couple of wonderful books dealing with various types of assumptions like this. One book, The Geography of Thought, contains a detailed experiment in which people from western and eastern cultural backgrounds were shown the same video of a marine scene in which a large fish was prominent. Afterwards, they were asked to describe what the scene had contained, what the visual "narrative" was about. The westerners did what I did -- they focused on the fish and followed it as a main focus. The people from eastern cultural backgrounds described the larger environment in great detail. When asked about the fish, most of them couldn't remember having seen it. The kinds of assumptions about what is and what isn't important become so second nature to us that we filter out everything else unconsciously. It takes a huge amount of attention and mental work to concentrate on these assumptions, and a huge amount of courage to re-examine and possibly challenge and change them. These are two reasons why I think it is so difficult to reach that thin band on the spectrum of intellectual challenge that MCT describes in the essay that began this thread.

 

I am remembering that when I used GEMS science with my elementary-aged dd and with a co-op, one of the explicitly stated aims of the program was to get kids to articulate their current understanding of how or why something in the physical world worked, complicate that understanding through a series of activities, guided discussion, free and structured experimentation, and the use of models; then kids would express in some way the way their ideas and thoughts had changed: for instance, their understanding of why the earth has seasons, before and after the activities. The GEMS authors point out that the actual reason for seasons is complex enough that many first year MIT students cannot accurately explain or articulate it; yet very young children can be helped to take the first steps toward dismantling their incomplete or inaccurate ideas and reforming them into more accurate understandings.

 

And furthermore, they can do this without the "bruising load" you mention now characterizing much of American high school education, Faith. The kids I taught were fascinated, engaged, and so completely involved that we consistently ran out of time; they didn't want to quit. A high quantitative level of reading and written output CAN accompany this level of thinking; but it need not do so. Reading books that seriously challenged some of my understandings about how people think or how the world works, or travel that involved contact with dramatically different lives in underdeveloped countries, or meeting people who made me question some of my ideas, were all in and of themselves relatively "easy" acts. It is changing, adapting, re-evaluating, or complicating your thinking that is so difficult and that can be so scary.

[Corraleno]

Underlying entrenched assumptions, be they intellectual or cultural, are the hardest kinds of things to re-examine and re-evaluate, partly because they are so much like the very air around us, so much taken for granted as universal and factual that we can barely even see them as constructions. The fear that MCT describes, which accompanies the thrill, is a reaction to the fracturing of our certainty about what is known and how we know it.

<snip>

... It is changing, adapting, re-evaluating, or complicating your thinking that is so difficult and that can be so scary.

:iagree:

 

This is how I interpreted MCT's quote, too — that mastering difficult content, even with "advanced levels of reading, abstraction, complexity, and pace" is not enough, but that the student has to pursue the material to a level that actually changes "the way they think of themselves."

 

For my kids, that may come through exploring the nature of being and knowing through philosophy and epistemology and through studying other cultures (and our own) anthropologically, since those are the areas where I have enough expertise to lead them to that "seam" MCT talks about. For another family, it might mean reading and analyzing difficult books — not just "difficult" in terms of the number of pages and level of vocabulary, but in terms of difficult themes and ideas that challenge their assumptions about themselves, the world, human nature, etc. To me, MCT isn't just talking about choosing the most difficult math text or taking the most AP courses; he's talking about students pushing themselves in ways that stretch their brains to think about things they've never thought about before, so that they "crack off the crusty shells of exoconcepts" and emerge a different person.

 

And I love the title: "Give Me Rigor or Give Me Mortis" :lol:

 

Jackie

[Joan in GE]

Thank you for this post/thread - it has the really challenging concepts that I'm only beginning to understand yet seek.

 

Above this, high up on the challenge continuum, there is a thin, almost unnoticeable band. It represents a level of rigor so challenging that beyond requiring students to study difficult content, it requires students to reconsider themselves. At this level, a small amount of fear creeps in. Rapid breathing ensues. The thrill factor jumps. Students not only do not know the material at all, they are not sure they are in the right place. They are not in Kansas anymore. Moses-like, they are intellectual strangers in a strange land. To answer the demands of the assignment, they must not only learn what is new, they must be what is new.

 

This is what happens for me with some of the threads on the WTM and in some relationships and spiritual studies at the moment - more than "subjects".

 

Master teaching, for gifted children, involves positioning the learning demands right at this seam, forcing students not only to learn, but to molt, to crack off the crusty shells of exoconcepts and get bigger. The unthreatening hard study in the level below is insufficiently rigorous because it builds their knowledge without developing their selves, and the really threatening impossibility in the level above is inappropriate because it will bruise them with failure, but between the difficult and the impossible is the rigorous."

 

This is a great challenge for our children...and a challenge for me to find where they can experience this and in what domain they really need this.

 

Thank you again,

Joan

[Tress]

Thank you, Diviya, for this awesome quote!

[8filltheheart]

The quote actually reminds me of the Bloom's Taxonomy. The lowest level being regurgitated facts w/little understanding attached. Fill in the blank w/names and dates.......all that is required is recognition and recall. Get to the top of the pyramid and students are having to make unique judgments and assess/evaluate/synthesize multiple criteria.

 

Most modern educational objectives fall into the knowledge category. The dependence on Scantron sheets is evidence of simple single answer/conclusion outcomes. Plug and chug textbooks fall into this category......give the student examples and then different numbers/situations which still follow the same pattern to replicate.

 

Classical education's goal is thought process/formation. Critical thinking is a main objective. (Um.....and doesn't that circle back around to what is rigor????:D:lol:)

[cathmom]

I find that quote interesting. I've read it now several times and I think there's something there that, on a fundamental level, I can't agree with. But I can't articulate what it is.

 

He's talking about gifted students. I was a gifted student. Very few things were hard for me (phonics was one - I didn't learn it until I taught it to my dc). In high school, which I attended for 3 years, I missed about 100 days and was still in the top 10% of my class. I was a National Merit Finalist and won a statewide English award and placed in a statewide Spanish competition. Spanish and French were the only subjects that I studied for. I did work in some classes in college and in graduate school.

 

His description of the highest level of challenge, which involves thrilling fear and a remaking of self, does not match my experience even in college and graduate school. Thrilling fear sounds unsettling and anxiety-producing, which does not sound to me like a way I would like to learn. It is not how I felt learning hard things. Again, I wonder how much of this is personality dependent.

 

The only thing I can think of that made me rethink "me" was reading some works of literature, mainly Kafka, but there have been others. I get wholly involved in my learning and enter a "flow" state of happiness and excitement.

 

I'm going to quote the last two paragraphs and bold what jumps out at me:

Above this, high up on the challenge continuum, there is a thin, almost unnoticeable band. It represents a level of rigor so challenging that beyond requiring students to study difficult content, it requires students to reconsider themselves. At this level, a small amount of fear creeps in. Rapid breathing ensues. The thrill factor jumps. Students not only do not know the material at all, they are not sure they are in the right place. They are not in Kansas anymore. Moses-like, they are intellectual strangers in a strange land. To answer the demands of the assignment, they must not only learn what is new, they must be what is new.

 

Master teaching, for gifted children, involves positioning the learning demands right at this seam, forcing students not only to learn, but to molt, to crack off the crusty shells of exoconcepts and get bigger. The unthreatening hard study in the level below is insufficiently rigorous because it builds their knowledge without developing their selves, and the really threatening impossibility in the level above is inappropriate because it will bruise them with failure, but between the difficult and the impossible is the rigorous

 

Maybe I have just never learned at this level and that is why I don't understand/agree. So have I spent 40 years not developing myself? I personally believe anxiety is counter-productive to learning.

 

Here are some quotes from my Teaching Philosophy:

 

We can see from observing a child that true learning occurs from an internal desire to master a subject. A teacher cannot provide this internal desire for an individual learner, but a teacher can either kindle or snuff out the desire that is already there. Children are born with an intense love of learning, and it is very hard to hold them back.

 

As a teacher, I try to create a comfortable, safe learning environment by showing respect to my students and by being firm and confident but friendly.

 

 

Thank you for posting and giving me some food for thought.