2025年10月28日 星期二

Writing to learn mathematics

 I have read a passage from William Zinsser's Writing to Learn. It reads: One day, I got a letter from a woman named Joan Countryman, who is head of the mathematics department at Germantown Friends School in Philadelphia. She had heard about my interest in writing across the curriculum. “For many years,” she said, “I’ve been asking my students to write about mathematics as they learned it, with predictably wonderful results. Writing seems to free them of the idea that math is a collection of right answers owned by the teacher—a body of knowledge that she will dispense in chunks and that they have to swallow and digest. That’s how most non-mathematicians perceive it. But what makes mathematics really interesting is not the right answer but where it came from and where it leads.” The letter grabbed my attention. Surely mathematics was a world of numbers. Could it also be penetrated with words? Could a person actually write sentences that would lead him through a mathematical problem and suggest further questions—different questions from the ones the teacher might raise? It had never occurred to me that the teacher wasn’t the sole custodian of mathematical truth, and it certainly never occurred to E. Grant Spicer, my elementary school math teacher, who so cowed me with his ownership of the right answer that I’ve had math anxiety ever since. To this day, I consider it a lucky month when I balance my checkbook, and the task is always accompanied by a slight pounding in my chest that I would otherwise take to be the onset of a heart attack. I still resent having to subtract a larger number from a smaller one by “borrowing” from the adjacent column. I resent it not only because I’m never sure I’ve done it right; I also seem to have to borrow more often than anyone else does. Why me?

ChatGPT 說:

Excellent — you’ve chosen one of the most memorable passages in Writing to Learn.

Zinsser’s reflection here captures a fundamental insight: writing is not just a way to record knowledge, but a way to discover it. Joan Countryman’s letter surprises him because it overturns the conventional belief that mathematics is purely about “right answers.” By having students write about math — explain where ideas come from, trace reasoning, and ask their own questions — she helps them move from passive receivers to active thinkers.

Here’s a concise breakdown of the key ideas and implications of the passage:

Theme / QuestionExplanation
Writing across the curriculumZinsser had promoted writing as a tool for learning in all subjects, not just English. Countryman’s example extends this to mathematics — the least expected area.
Freedom through writingWriting “frees” students from the notion that math knowledge is owned by the teacher. It gives them intellectual ownership and invites curiosity.
Zinsser’s self-reflectionHe admits that he had always seen math as belonging to the teacher — “the sole custodian of mathematical truth.” His own math anxiety shows how teaching style can suppress confidence.
Tone and styleThe passage begins factually (a letter), turns curious (“Surely mathematics was a world of numbers”), becomes personal and humorous (“I resent having to borrow”), and ends in self-irony. This personal voice illustrates how writing itself helps him think.
Underlying messageThinking through writing transforms subjects — even the most rigid ones — into fields of exploration. Writing is not just a medium of expression but a method of learning how to think.

If you’d like, I can:

  1. Align this English passage with a Traditional Chinese translation sentence by sentence,

  2. Or, analyze it sentence by sentence in terms of grammar, semantics, and pragmatics.

Which would you prefer next?

你說:
I like both, but the first comes first, then comes the second. OK?
ChatGPT 說:

Perfect — that’s an excellent order:
English–Traditional Chinese sentence alignment, then
Grammar, semantics, and pragmatics analysis for each sentence.

Let’s begin with Part 1: sentence-by-sentence bilingual alignment of the passage you quoted from Writing to Learn by William Zinsser.


🟩 Part 1 — Bilingual Alignment

EnglishTraditional Chinese 翻譯
One day, I got a letter from a woman named Joan Countryman, who is head of the mathematics department at Germantown Friends School in Philadelphia.有一天,我收到一封來自一位名叫瓊.康特里曼女士的信,她是費城日耳曼鎮友誼學校數學系的主任。
She had heard about my interest in writing across the curriculum.她聽說我對「跨學科寫作」這個理念很感興趣。
“For many years,” she said, “I’ve been asking my students to write about mathematics as they learned it, with predictably wonderful results.她說:「多年來,我一直要求學生在學習數學的同時寫下他們的想法,結果一如預期地非常好。
Writing seems to free them of the idea that math is a collection of right answers owned by the teacher—a body of knowledge that she will dispense in chunks and that they have to swallow and digest.寫作似乎使他們擺脫了這樣的觀念:數學是一套由老師所擁有的正確答案的集合——一種她會分段傳授、而學生必須吞下並消化的知識體系。
That’s how most non-mathematicians perceive it.這正是大多數非數學家對數學的看法。
But what makes mathematics really interesting is not the right answer but where it came from and where it leads.”但真正讓數學有趣的,並不是正確答案,而是答案的來源與它所引向的方向。」
The letter grabbed my attention.這封信引起了我的注意。
Surely mathematics was a world of numbers.當然,數學是一個數字的世界。
Could it also be penetrated with words?它也能被文字所穿透嗎?
Could a person actually write sentences that would lead him through a mathematical problem and suggest further questions—different questions from the ones the teacher might raise?一個人真的可以用句子引導自己解決數學問題,並提出進一步的問題——那些與老師所提問題不同的問題嗎?
It had never occurred to me that the teacher wasn’t the sole custodian of mathematical truth,我從來沒想過老師並不是數學真理的唯一守護者,
and it certainly never occurred to E. Grant Spicer, my elementary school math teacher, who so cowed me with his ownership of the right answer that I’ve had math anxiety ever since.這一點當然也從未出現在我的小學數學老師E.葛蘭特.斯派瑟的腦海中;他以自己對正確答案的掌控嚇得我從此對數學心生焦慮。
To this day, I consider it a lucky month when I balance my checkbook,直到今天,只要我能對上支票簿的帳,就覺得那是幸運的一個月,
and the task is always accompanied by a slight pounding in my chest that I would otherwise take to be the onset of a heart attack.而這項工作總會伴隨著胸口微微的悸動,若不是知道原因,我會以為那是心臟病發作的前兆。
I still resent having to subtract a larger number from a smaller one by “borrowing” from the adjacent column.我至今仍對「從相鄰的欄位借位以便用小數減大數」這件事心懷不滿。
I resent it not only because I’m never sure I’ve done it right;我不滿,不只是因為我從來不確定自己是否做對了;
I also seem to have to borrow more often than anyone else does.我似乎也比別人更常需要借位。
Why me?為什麼偏偏是我?

Would you like me to proceed now with Part 2 — grammar, semantics, and pragmatics analysis, sentence by sentence?

你說:
Yes, please.
ChatGPT 說:

Excellent 👍 Let’s begin Part 2 — Grammar, Semantics, and Pragmatics Analysis of the same passage.
Each sentence below is analyzed in three layers:

  • Grammar → sentence structure, parts of speech, clause relations.

  • Semantics → literal and implied meaning.

  • Pragmatics → writer’s intention, tone, and communicative effect.


1️⃣

Sentence:
One day, I got a letter from a woman named Joan Countryman, who is head of the mathematics department at Germantown Friends School in Philadelphia.

Grammar:

  • Main clause: I got a letter (S + V + O).

  • Prepositional phrase from a woman … Philadelphia modifies letter.

  • Relative clause who is head … describes woman.

Semantics:
Introduces a specific incident and identifies Joan Countryman and her position. Establishes credibility (authority in mathematics).

Pragmatics:
Sets up the story’s trigger and builds ethos; the use of full title and location adds realism and trustworthiness.


2️⃣

Sentence:
She had heard about my interest in writing across the curriculum.

Grammar:

  • Past perfect had heard → an earlier action preceding the main event.

  • Prepositional phrase about my interest … functions as the object of heard.

Semantics:
Shows causal connection: she writes because she already knew his reputation.

Pragmatics:
Smooth transition; creates continuity and rapport between two educators.


3️⃣

Sentence:
“For many years,” she said, “I’ve been asking my students to write about mathematics as they learned it, with predictably wonderful results.”

Grammar:

  • Reporting frame she said encloses direct quotation.

  • Present perfect progressive I’ve been asking emphasizes ongoing practice.

  • Prepositional phrase with predictably wonderful results → adverbial of manner/result.

Semantics:
Expresses habitual pedagogical strategy and its positive outcomes.

Pragmatics:
Her confident tone lends authority; quotation introduces another voice to reinforce the main idea of “writing to learn.”


4️⃣

Sentence:
Writing seems to free them of the idea that math is a collection of right answers owned by the teacher—a body of knowledge that she will dispense in chunks and that they have to swallow and digest.

Grammar:

  • Main clause: Writing seems to free them of the idea …

  • Complement clause that math is … → object of idea.

  • Two coordinated relative clauses modify a body of knowledge.

Semantics:
Writing liberates students from passive learning; math becomes personal reasoning rather than memorization.

Pragmatics:
Metaphors “swallow and digest” dramatize mechanical learning; gendered “she” humorously portrays the teacher as dispenser of facts.


5️⃣

Sentence:
That’s how most non-mathematicians perceive it.

Grammar:

  • Deictic That’s = “That is.”

  • Clause how … perceive it → complement.

Semantics:
Summarizes common misconception: outsiders see math as fixed answers.

Pragmatics:
Establishes shared ground with readers likely outside mathematics.


6️⃣

Sentence:
But what makes mathematics really interesting is not the right answer but where it came from and where it leads.”

Grammar:

  • Interrogative structure used declaratively: what makes … is not A but B.

  • Two coordinated prepositional phrases form contrastive complement.

Semantics:
Defines true mathematical value as process and discovery, not results.

Pragmatics:
Pedagogical inversion challenges conventional wisdom; persuasive and reflective tone.


7️⃣

Sentence:
The letter grabbed my attention.

Grammar:
Simple past active clause. grabbed = transitive verb.

Semantics:
Marks the turning point from quotation to narrator’s reaction.

Pragmatics:
Energetic verb “grabbed” enlivens narrative, signaling personal engagement.


8️⃣

Sentence:
Surely mathematics was a world of numbers.

Grammar:

  • Declarative sentence with adverb Surely (expresses assumption).

  • Copular verb was links subject and complement.

Semantics:
Reveals Zinsser’s initial, naïve assumption.

Pragmatics:
Self-mocking tone; sets up contrast for his coming revelation.


9️⃣

Sentence:
Could it also be penetrated with words?

Grammar:
Interrogative using modal could; passive construction.

Semantics:
Poses central metaphor: language penetrating numbers.

Pragmatics:
Invites reader’s curiosity; rhetorical question marking conceptual shift.


🔟

Sentence:
Could a person actually write sentences that would lead him through a mathematical problem and suggest further questions—different questions from the ones the teacher might raise?

Grammar:

  • Complex interrogative with relative clause that would lead … and suggest …

  • Dash introduces appositive elaboration.

Semantics:
Explores potential of writing as reasoning tool generating independent inquiry.

Pragmatics:
Cumulative syntax mirrors the process of thought; open-ended questioning draws readers into speculation.


11️⃣

Sentence:
It had never occurred to me that the teacher wasn’t the sole custodian of mathematical truth,

Grammar:

  • Idiomatic expression It had never occurred to me that …

  • Complement clause that the teacher wasn’t … → object.

Semantics:
Admission of limited perspective and dependence on authority.

Pragmatics:
Creates humility and credibility; prepares contrast with next sentence.


12️⃣

Sentence:
and it certainly never occurred to E. Grant Spicer, my elementary school math teacher, who so cowed me with his ownership of the right answer that I’ve had math anxiety ever since.

Grammar:

  • Coordinated with previous sentence by and.

  • Relative clause who so cowed me … that … → cause-result construction.

Semantics:
Identifies personal source of anxiety; long embedded clause shows emotional weight.

Pragmatics:
Blends humor and confession; humanizes abstract discussion through vivid memory.


13️⃣

Sentence:
To this day, I consider it a lucky month when I balance my checkbook,

Grammar:

  • Time adverbial To this day marks continuity.

  • Subordinate clause when I balance … modifies month.

Semantics:
Shows enduring consequence of early fear; even simple arithmetic feels miraculous.

Pragmatics:
Self-deprecating humor softens criticism and invites empathy.


14️⃣

Sentence:
and the task is always accompanied by a slight pounding in my chest that I would otherwise take to be the onset of a heart attack.

Grammar:

  • Coordinated with previous clause.

  • Relative clause that I would otherwise take … modifies pounding.

Semantics:
Physiological metaphor of anxiety.

Pragmatics:
Comic exaggeration conveys both truth and irony; maintains reader engagement.


15️⃣

Sentence:
I still resent having to subtract a larger number from a smaller one by “borrowing” from the adjacent column.

Grammar:

  • Verb resent + gerund phrase having to subtract … as object.

  • Quotation marks mark technical term humorously.

Semantics:
Expresses lingering frustration toward arithmetic operations.

Pragmatics:
Symbolic complaint—childhood helplessness persists into adulthood; humor masks vulnerability.


16️⃣

Sentence:
I resent it not only because I’m never sure I’ve done it right;

Grammar:

  • Parallel connector not only because … ; next clause (17) completes but also …

Semantics:
Begins a double-cause construction showing dual reasons for resentment.

Pragmatics:
Suspenseful semi-colon keeps rhythm; conversational tone.


17️⃣

Sentence:
I also seem to have to borrow more often than anyone else does.

Grammar:

  • Auxiliary chain seem to have to borrow → modality of perception + necessity.

  • Comparative more often than anyone else does.

Semantics:
Hyperbolic self-comparison; perception of unique misfortune.

Pragmatics:
Ends humorously; shifts from confession to comic relief.


18️⃣

Sentence:
Why me?

Grammar:
Elliptical interrogative; subject + predicate implied (Why is it me?).

Semantics:
Expresses rhetorical despair.

Pragmatics:
Concludes passage with irony and warmth—an emotional echo of every anxious student.


Would you like me next to synthesize these analyses into a summary of the pedagogical insight and rhetorical craft Zinsser demonstrates here (how writing and storytelling serve his teaching argument)?

您希望我接下來將這些分析綜合成對 Zinsser 在這裡展示的教學洞察力和修辭技巧的總結嗎(寫作和講故事如何服務於他的教學論點)?

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