Above and Below: When Abstract Thinking Comes to Life

Nov 18, 2024

Sometimes teachers have a tendency to underplay the importance of abstract vocabulary as tools of cognition. One instructional mistake I made when I began teaching middle school English was assuming my students would know what I meant by the word “coordinate” when they could define it in a plausible way: “things of the same order” or “knife and fork” or “co-” equals “together or with” and “ordinate” means “order.” It was when I taught outlining as a literacy technique it hit me like a ton of bricks. Where there is a Roman Numeral I and you have an A, you have to have a B. Why did I see so many IA, IIA, IIIABs?

My mistake was thinking that learning a definition of a metalinguistic word meant understanding the word. Knowing that “knife and fork” are coordinate, that “kitchen utensils” are superordinate is a sophisticated form of metalinguistic analysis. Metalinguistic awareness is visible at four levels: 1) surface definition, 2) example recognition, 3) active application in analysis, and 4) understanding deep structure.

The first level is assessable by multiple choice, matching, or fill-in-the-blank. Level two is assessable through the same methods expanded to include short constructed responses. Level three is assessable by asking students to examine prepared samples of language and use the tools to explain hierarchical relations. Level four is assessable in discussions that self-consciously focus on hierarchical structures both abstractly and with specific examples.

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Part of the challenge at level four stems from the multiplicity of abstract structures coordinate with hierarchical structure. It’s not the only book on the shelf. There are other structural relations which are features of language beyond hierarchy. Consider a much simpler structure: Sequence or chronology.

Rather than exist in hierarchies, some words function as markers of sequence. Terms of hierarchy and terms of sequence are in a coordinate relationship in that hierarchy and sequences have their own ways to signal relations among ideas. Subordinate terms of sequence are first, second, third; before and after; meanwhile. Hyponyms1 ranking below these subordinate terms are just now; moments ago; last week; previously.

In this post I focus on hierarchical relationships for two reasons. First, students with a deep understanding of hierarchical structure have considerably more capacity to organize their own academic writing and to comprehend the texts produced by others, particularly scientific writing. In a similar manner, students with deep understanding of sequence and a subordinate category, cause and effect, display heightened capacity to compose and comprehend historical and mathematical text.

The following examples probably require level four capacity. I’m personifying Superordination, Coordination, Hyponyms, Hypernyms, and Hyperordination in the examples to create fantasy narratives with an anchor in concrete. I think asking students to read and discuss examples like these and then write their own could be interesting. Assigning them examples to discuss in pairs, answer the questions, and then checkthe fruits of discussion with an LLM followed by a quick self-assessment might be worth a thought.

Your task? Explore the implied hierarchical structure in each example.

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Superordination was sad. The kids on the playground wouldn’t let him join in their reindeer games. He wanted to play tetherball so badly. His teacher saw him moping and talked with him. As gently as she could, she communicated to him: “Being above it all isn't the way to make friends.”

Discussion Question: What about this example suggests a meaning for the word superordination? Can Superordination change his behavior?

Superordination met Hyponymy at a speed dating event. As a bit of an egghead, Superordination had trouble meeting potential partners. Hyponymy had a head shaped like a hammer, the impact surface like a prominent nose, the claw for pulling nails sticking up like a Mohawk hairdo. Their skin looked wooden. “I reside at the Tool Chest Hotel,” Hyponym said. “I know a couple who live there,” Superordinate said with a crooked smile. “Phillip Screwdriver and Allen Wrench.”

Discussion question: Hyponymy lives at the Tool Chest Hotel. This clue suggests the meaning of hyponym and hyponymy. Define and give an original example of hyponym.

Superordination applied for a job in a shoe store. After the interview, they walked back to their apartment and called a friend to commiserate. They just knew they weren’t going to get hired.

“Oh, I think you’re equal to the task of selling shoes,” Coordination said. “I know Shoe Shine pretty well and their helper, Polish Cloth. Why don’t I put in a good word for you?”

"I said I could categorize their inventory into a taxonomic delight like no other shoe store—loafers subordinate to casual shoes, stilettos a subset of formal wear, sneakers tucked into running, walking, and cross-training subtypes. The manager laughed at me and said they needed someone who could match shoes with feet.”

“Well, that’s rude,” said Coordination.

Discussion Question: Superordinate’s mistake is very similar to the mistake Superordinate made on the playground in the first example. Explain how. Define coordination.

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Superordination was enjoying the early sunshine in the rose garden of the bed and breakfast near Ocean Avenue in Carmel, watching Monterey pines peek through the fog beginning to lift.

The white-washed cottage with its climbing roses perfectly embodied what city ordinances demanded, keeping the village's ultra-expensive quaintness intact. A few early tourists were already strolling along the garden's white picket fence in search of coffee and croissants. Likely they were heading toward the art galleries, clothing boutiques, and curiosity shops on Ocean Avenue. A slightly salty scent of fresh-baked pastries wafted from Carmel Bakery just down the street.

A very old woman stopped along the fence and stared longingly at Superordination.

“Do I know you?” asked Superordination.

She remained unmoving in her position at the fence, stoically staring, tears beginning to glisten in her eyes. Her snow-white hair moved in a gentle breeze.

“Do I know you, Ma’am?”

“Apparently not,'“ she said, as if shaking herself from a trance. “But I know you. I’ve been looking for you for Ages.”

Strange, thought Superordination. Where have I seen this old woman before?

“Where have we met?”

“I lost track of you over a century ago,” she said. “I thought I’d found you once in 1953 when I was visiting the Cavendish Laboratory at the University of Cambridge. Two gentlemen scientists needed my help, one named Watson, the other Crick.”

“You actually met Watson and Crick, the discoverers of our DNA Genome, among the most magnificent structures in the world, the Queen of Hierachies!?”

“It was a happy accident,” the old woman said. “Like finding you here. You really don’t remember me?”

Superordinate paused and thought really hard.

“It’s you! Are you… my grandmother?”

“That I am,” said the old woman with a charming lilt. “Grandma Hyperordinate.”

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Just as DNA embodies life's grand taxonomy, Grandma Hyperordinate's visit to Carmel brings the narrative full circle. She represents the highest order of classification, the matriarch of organizational thinking, the title of an essay, the abstract of a study. Her role in Watson and Crick's discovery and in her grandchild Superordination's life suggests that understanding hierarchical relationships isn't just academic. It’s fundamental to how we decode the natural world and human knowledge.

This story, like a well-structured outline, shows that true understanding requires moving beyond simple definitions to see the intricate dance between levels of meaning, from the concrete details of a Carmel morning to the abstract heights of taxonomic thinking.

Learning to Read, Reading to Learn

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