contradictions

In an earlier post, I wrote,

It is not the structure of the five-paragraph essay that is limiting: It is a lack of critical reflection on one's ideas.

Many apparently disagree with that assertion, at least about the part on structure being limiting. I'm not sure why they do. Perhaps it's because many do use the five-paragraph essay in limiting ways. Perhaps it comes from a notion of learning as a creative endeavor, and perhaps the notion of "creative" for many suggests that learning occurs by intuitive leaps and bounds, which structure unduly restrains. However, without structure, no creativity can take place. Language itself requires structure to communicate meaning. In English, for example, stress can differentiate between adjectives and compound nouns, as in the difference between a "blue bird" (a bird that is blue in color) and a "bluebird" (a particular type of bird).

learning never occurs de novo.

Similarly, structure is crucial for learning. After all, learning never occurs de novo. Rather,

  • Learning always builds upon that which came before, and
  • Learning almost always involves a remixing of known building blocks.

My favorite example of these two principles is the many species that have evolved from the remixing of only four building blocks of DNA.

In looking at the five-paragraph essay, we can see at least four potential building blocks of writing:

  • introduction
  • "main idea" (thesis statement and topic sentence)
  • evidence
  • explanation (explanation of evidence and conclusion)

Let's look at how these four building blocks are used across three different situations: (1) framing a quotation, (2) the five-paragraph essay, and (3) introducing an academic journal article.

When introducing a quotation, as Graff and Birkenstein note in their book "They Say / I Say", it is typically framed. First, one introduces the source/author of the quotation and the author's main claim, then the quotation (evidence), and next one explains the quotation in light of the author's claim. Then, one uses the framed quotation to introduce one's own position (claim), thus starting another cycle of introduction, claim, evidence, and explanation.

In the five-paragraph essay, of course, one introduces the main claim (thesis statement), provides evidence for that claim in the form of subclaims (topic sentences), explains the subclaims with more evidence and explanations (logic or reasoning), and finally re-explains the main claim in the conclusion.

In introductions to academic journal articles, John Swales has shown that regardless of discipline they always include four rhetorical moves: introduce the topic, review the literature on that topic (explain the topic and the evidence surrounding it), indicate a gap in the literature (explain how something is missing or wrong in the literature, a claim accompanied by evidence and explanation), and then explain what one will do to remedy that gap (another claim with the evidence and further explanation forthcoming in the rest of the article).

The building blocks naturally take different forms in each context and build upon one another as the context becomes more complex. The power of such an approach is its interlocking strength of basic concepts across contexts, thus facilitating learning and transfer via student use and practice of building block concepts across different writing landscapes.

Thus, again, although one can use structure in limiting ways, when used appropriately, structure supports learning. For those who use the five-paragraph essay, then, rather than treat the structure as a formula, it would be more fruitful to familiarize students with its building blocks across contexts (including the five-paragraph essay), rearranging the building blocks in different orders and combinations to consider their rhetorical effect.

To acquaint students with these building blocks, consider beginning by building upon their own experiences with conversation. For example,

  1. First, have students write a conversation they might have with friends trying to persuade them to see a certain movie, play a particular game, or do some other activity, keeping in focus that their friends want to see a different movie or play a different game.
  2. Next, have them analyze their conversations, asking questions such as:
    • Are the building blocks of introduction, claim, evidence, and explanation there?
    • Are there other building blocks?
    • Are they consistently in a particular sequence?
    • Does the order of building blocks change?
    • Is a particular sequence of building blocks more effective?
    • When?
    • Why?
    • How do the sequences and uses of building blocks in conversations compare/contrast to those in the five-paragraph essay?

Of course, you can extend this process of analysis to other genres, such as blogs and editorials in newspapers, and to other media, such as podcasts and videos.

contradictions ... are the driving force of learning.

Whether learning new languages or new dialects, such as academese and blogese, this process of analyzing concepts across contexts can bring into focus contradictions between the rhetorical conventions of different dialects, languages, disciplines, and media. And it is contradictions that are the driving force of learning.

Related posts:
The Five-Paragraph Essay (continued)
The Five-Paragraph Essay
Click on building blocks and contradictions under Topics.
See also my article in Complicity: "Building Blocks and Learning".

Jay Mathews, in "New teacher jolts KIPP", writes about Lisa Suben, a new teacher in the KIPP schools, who had her math students jump from the 16th to the 77th percentile in a single year. That's an unbelievably huge jump! How'd she do it? Theoretically, she says:

"My primary goal as a teacher is to help my students understand the reasoning behind math rules and procedures. I have several core beliefs about this: (1) Understanding is constructed by the learner, not passively received from the teacher. (2) Understanding is built by making connections between as many strands of knowledge as possible. (3) Understanding is galvanized through communication. (4) Understanding is only valuable when you reflect on it and question it."

Items (2) and (3) are related. That is, communication can (but need not) present more strands of knowledge to enter the picture that allows more connections to be made. It's not the connections per se that build understanding but rather the contradictions among them. Contradictions are the driving force of learning. On item (4), reflecting and questioning can improve one's understanding, of course, but most understanding is unconscious. That doesn't make it unvaluable.

Suben translated her theory into the following practice:

The core of her method is the workbook she produced last year on the fly. It "lets students build their own notes and create their own examples. It is incredibly active learning," she said. They were encouraged to write down the meaning of important terms and strategies they used that worked with certain kinds of problems.

Suben, I imagine, is differentiating between a traditional lecture form of teaching and Deweyan "learning by doing". It's not clear that one type of learning is more active than another. All learning is active. Of course, I can also imagine that students focus more on something they are "doing" as opposed to "receiving," and thus they spend more "effective time on task," the crucial element in learning. Thus, Suben's having her students create their own notes, examples, and meaning is an excellent way to (1) focus them more effectively on the tasks at hand and (2) bring them into contradictions between their declarative and procedural knowledge (see ACT-R Theory) and so improve their understanding.

Related posts on the five-paragraph essay:
Forget IQ. Just Work Hard!
The Expert Mind
Learning: A State of Disatisfaction
Learning with Examples

The Ornament

When you think of tolerance and multiculturalism, does Medieval Europe come to mind? Probably not. Yet, Maria Rosa Menocal's (professor of Spanish and Director of the Whitney Humanities Center at Yale University) book The Ornament of the World: How Muslims, Jews, and Christians Created a Culture of Tolerance in Medieval Spain makes precisely that claim. Weaving together tales from medieval Spain, Menocal illustrates how three different religions built a "first-rate" culture of tolerance that influenced Europe for centuries to come.

Menocal intertwines "culture of tolerance" with F. Scott Fitzgerald's notion of a "first-rate" mind, writing,

the test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time ...

[that] contradictions--within oneself, as well as within one's culture--could be positive and productive. (pp. 10-11)

Contradictions, Menocal asserts, were responsible for the flowering of art, intellect, and tolerance towards others in Medieval Spain: Muslims, Christians, and Jews interacted openly and freely, keeping a strong sense of identity, yet assimilating features of other cultures that they admired. In Medieval Spain, tolerating contraries led to great philosphers like ibn Rusd and Maimonides, who wrestled with the contraries of faith and reason. Maimonides, with his Second Law, or Mishneh Torah, would be called a "second Moses." Moses of Leon struggled with the traditional Halakah and came up with his Sefer ha-zohar, The Book of Splendor, a systematic compilation of Kabbalah, the Jewish mystical tradition. The study of the living language of Arabic generated once again a Hebrew that was "the language of a vibrant, living poetry" (p. 109).

Such "first-rate" contraries resulted in "authentic multiculturalism." Jews, such as Hasdai ibn Shaprut and Samuel the Nagid, were viziers in an Islamic government. Alongside Arabic--a language of state, love, and religion--existed other religious and vernacular languages. This multicultural environment preferred freedom of religious expression to political correctness; "incongruity in the shaping of individuals" (p. 11) to a "strict harmony of ... cultural identities" (p. 277); "to pose difficult questions rather than to propose easy answers or facile morals" (p. 274); and so on. All of these contraries and others touch upon so many issues in education and modern life, such as assimilation vs. heritage maintenance, multiculturalism vs. traditional canons, political correctness vs. freedom of expression and of religion, bilingual education vs. immersion, and so on.

The authentic multiculturalism of Medieval Spain arose from tolerance of and dialogue with others. Yet, tolerance and dialogue are not givens, as this culture of tolerance eventually fell.

WHAT HAPPENED? HOW AND WHY DOES A CULTURE OF tolerance fall apart? How did a people come to abandon a culture rooted in an ethic of yes and no, so readily able to love and embrace the architecture or the poetry of political enemies or religious rivals, so willing to read good books regardless of the library they came from? All the answers are themselves bundles of contradictions.... Perhaps all that can be said with any conviction is that in the combination of spectacular successes and failures presented by this history lie tales of both warning and encouragement. (p. 266)

The notion of contradictions being essential for tolerance and creativity, and also for learning (see Learning: A State of Dissatisfaction) underscores the need to inject uncertainty and novelty into the classroom, not so much as to be overwhelming but enough to promote the flow of learning.

At the end of the book, Menocal writes, "Every reader will take away different lessons from the tales in this book." Indeed.

Below are some reviews that offer other readings of and lessons from The Ornament of the World

A few weeks ago, my wife related to me these questions from our son when he learned she was expecting:

Son (to mom): "How did the baby get there? Did you eat him?"

Similar to the story of the three blind men stating their opinions of the elephant's nature, academic theories derive from interpretations of experience--not from objective perceptions of reality.

I noted this earlier in "Is there anything new under the sun?"

learning to write involves a process of reflecting and acting on contradictions between students’ existing schemas and their present experiences.

... The concept of viability reminds us that reality cannot be directly perceived.

Although learning anything is a processing of resolving contradictions, or in Piaget's terms, a process of equilibrating between assimilation and accommodation, that learning remains an adaptation to experience rather than an insight into reality.

This is not an "anything goes" theory. Try jumping off the Empire State Building. Rather, it's acknowledging that at best we "see in a mirror dimly." What I'm wondering is how we apply this theoretical perspective practically to our other theories. When we say to "listen carefully" to our students, do we really see with more light?

Here's an interesting story from Idries Shah's book Tales of the Dervishes:


One dark night a dervish was passing a dry well when he heard a cry for help from below. 'What is the matter?' he called down.

'I am a grammarian, and I have unfortunately fallen, due to my ignorance of the path, into this deep well, in which I am now all but immobilized.' responded the other.

'Hold, friend, and I'll fetch a ladder and rope,' said the dervish.

'One moment please!' said the grammarian. 'Your grammar and diction are faulty; be good enough to amend them.'

'If that is so much more important than the essentials,' shouted the dervish, 'you had best stay where you are until I have learned to speak properly.'

And he went his way.


This story reminds me of the psychology study, which I mentioned in an earlier posting, "Emotion overrules reason," that found that staunch Democrats and Republications are "both adept at ignoring facts,"

The study points to a total lack of reason in political decision-making.

As someone said thousands of years ago, "There is nothing new under the sun" (Ecclesiastes 1:9), at least when it comes to understanding human behavior. Our pet theories can "immobilize" us, preventing us from seeing others' perspectives (see again "Everybody's an Expert" by Louis Menand).

So, where does this take us? For me, I return to a paper I wrote on the application of radical constructivism to writing in another language. Radical constructivism is based on Jean Piaget's work and is a perspective on knowing by Ernst von Glasersfeld, who asserted that knowledge is constructed actively by an individual in a way that fits one's experience, that provides a viable explanation of one's experience.

In looking at how students learn, many simply accept that learning is "merely a straightforward process of building upon students’ prior experiences and filling in schemas with new data, or knowledge. Rather, learning to write involves a process of reflecting and acting on contradictions between students’ existing schemas and their present experiences."

In looking at how teachers interact with students, we might believe "that these contradictions should be resolved in favor of the teacher’s “correct” model. The concept of viability reminds us that reality cannot be directly perceived. Teachers, as well as students, construct models representing their experiences rather than an actual reality. Thus, the student’s schema may not only be coherent according to his or her experiences but may also be insightful and effective. ... [Thus], we must listen closely to hear what is productive in the students’ models and build from there (Confrey, 1991, 1998)."

So, although this notion may not be new, still it is worth repeating: Listening may be a instructor's most valuable asset for learning how to teach.