[User]
Which numbered sense of "learn" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: No one in his right mind actually believes that we all have an equal academic potential. -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "<t>learning</t> "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline.

Senses:
1. definition=gain knowledge or skills | synonyms=larn, acquire | examples=She learned dancing from her sister; I learned Sanskrit
2. definition=get to know or become aware of, usually accidentally | synonyms=hear, get word, get wind, pick up, find out, get a line | examples=I learned that she has two grown-up children; I see that you have been promoted
3. definition=commit to memory; learn by heart | synonyms=memorize, memorise, con | examples=Have you memorized your lines for the play yet?
4. definition=be a student of a certain subject | synonyms=study, read, take | examples=She is reading for the bar exam
5. definition=impart skills or knowledge to | synonyms=teach, instruct | examples=I taught them French; He instructed me in building a boat
6. definition=find out, learn, or determine with certainty, usually by making an inquiry or other effort | synonyms=determine, check, find out, see, ascertain, watch | examples=I want to see whether she speaks French; See whether it works

reasoning_content:
1.  **Analyze the Request:** The user wants to identify which numbered sense of the word "learn" (marked as `<t>learning</t>`) is used in the provided context. The output must be *only* the number.

2.  **Locate the Target Word:** The target word is `<t>learning</t>` in the phrase: "...with students who ca not add or subtract 'learning' the conceptual basis of mathematical theory..."

3.  **Analyze the Contextual Usage:**
    *   The phrase is: "students who ca not add or subtract 'learning' the conceptual basis of mathematical theory."
    *   The structure suggests that "learning" is being used as a verb or a gerund/noun describing the *process* or *act* of acquiring knowledge (the conceptual basis).
    *   The context contrasts the ability to perform basic arithmetic (add or subtract) with the ability to grasp the underlying theory.
    *   The phrase "add or subtract learning the conceptual basis" is slightly awkward, but it implies that they cannot *incorporate* or *understand* the theoretical foundation.

4.  **Evaluate the Senses of "Learn":**

    *   **Sense 1:** definition=gain knowledge or skills | synonyms=larn, acquire | examples=She learned dancing from her sister; I learned Sanskrit. (Focuses on the acquisition of knowledge/skills.)
    *   **Sense 2:** definition=get to know or become aware of, usually accidentally | synonyms=hear, get word, get wind, pick up, find out, get a line. (Focuses on incidental discovery.)
    *   **Sense 3:** definition=commit to memory; learn by heart | synonyms=memorize, memorise, con. (Focuses on rote memorization.)
    *   **Sense 4:** definition=be a student of a certain subject | synonyms=study, read, take. (Focuses on the state of being a student.)
    *   **Sense 5:** definition=impart skills or knowledge to | synonyms=teach, instruct. (Focuses on the action of the teacher.)
    *   **Sense 6:** definition=find out, learn, or determine with certainty, usually by making an inquiry or other effort | synonyms=determine, check, find out, see, ascertain, watch. (Focuses on investigation/verification.)

5.  **Match the Usage to the Sense:**
    *   The students are failing to grasp the "conceptual basis of mathematical theory." This is a failure to *acquire* or *gain* the necessary knowledge.
    *   Sense 1 ("gain knowledge or skills") perfectly matches the idea of acquiring a conceptual basis or theoretical understanding.

6.  **Conclusion:** Sense 1 is the correct fit. (The students cannot *acquire* the conceptual basis.)


attempt_kind: initial

status: success

[User]
Which numbered sense of "basis" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: No one in his right mind actually believes that we all have an equal academic potential. -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual <t>basis</t> of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline.

Senses:
1. definition=a relation that provides the foundation for something | synonyms=footing, ground | examples=they were on a friendly footing; he worked on an interim basis
2. definition=the fundamental assumptions from which something is begun or developed or calculated or explained | synonyms=base, foundation, fundament, groundwork, cornerstone | examples=the whole argument rested on a basis of conjecture
3. definition=the most important or necessary part of something | synonyms=base | examples=the basis of this drink is orange juice

finish_reason: stop

role: assistant

reasoning_content:
1.  **Analyze the request:** The user wants to identify which numbered sense of the word "basis" (marked with `<t></t>`) is used in the provided context. The output must be *only* the number.

2.  **Locate the target word in the context:**
    "...with students who ca not add or subtract "learning "the conceptual <t>basis</t> of mathematical theory..."

3.  **Analyze the context surrounding the target word:** The phrase is "the conceptual basis of mathematical theory."

4.  **Determine the meaning of "basis" in this specific phrase:** When discussing a theory, the "basis" refers to the fundamental principles, assumptions, or underlying structure upon which that theory is built.

5.  **Evaluate the provided senses:**

    *   **Sense 1:** definition=a relation that provides the foundation for something | synonyms=footing, ground | examples=they were on a friendly footing; he worked on an interim basis. (This relates to relationships or temporary arrangements, not the core structure of a theory.)
    *   **Sense 2:** definition=the fundamental assumptions from which something is begun or developed or calculated or explained | synonyms=base, foundation, fundament, groundwork, cornerstone | examples=the whole argument rested on a basis of conjecture. (This perfectly matches the idea of the fundamental principles/assumptions of a mathematical theory.)
    *   **Sense 3:** definition=the most important or necessary part of something | synonyms=base | examples=the basis of this drink is orange juice. (While related to importance, this sense usually refers to a single component or ingredient, not the entire conceptual framework of a theory.)

6.  **Conclusion:** Sense 2 is the correct meaning.

7.  **Format the output:** Return only the number.

currency: USD

source: unavailable


[User]
Which numbered sense of "mathematical" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: No one in his right mind actually believes that we all have an equal academic potential. -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of <t>mathematical</t> theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline.

Senses:
1. definition=of or pertaining to or of the nature of mathematics | examples=a mathematical textbook; slide rules and other mathematical instruments
2. definition=relating to or having ability to think in or work with numbers | synonyms=numerical | examples=tests for rating numerical aptitude; a mathematical whiz
3. definition=beyond question | examples=a mathematical certainty
4. definition=statistically possible though highly improbable | examples=have a mathematical chance of making the playoffs
5. definition=characterized by the exactness or precision of mathematics | examples=mathematical precision

reasoning_content:
1.  **Analyze the Request:** The user wants to identify which numbered sense of the word "mathematical" is used in the provided context. The output must be *only* the number.

2.  **Locate the Target Word and Context:**
    *   Target phrase: "learning 'the conceptual basis of <t>mathematical</t> theory'"
    *   The context discusses students who "ca not add or subtract" and are struggling with the "conceptual basis of mathematical theory."

3.  **Analyze the Meaning in Context:**
    *   "Mathematical theory" here refers to the fundamental concepts, principles, and structures that constitute the field of mathematics itself (e.g., algebra, calculus, number theory).
    *   The students are failing to grasp the *nature* or *definition* of the concepts being taught.

4.  **Evaluate the Senses:**

    *   **Sense 1:** definition=of or pertaining to or of the nature of mathematics | examples=a mathematical textbook; slide rules and other mathematical instruments.
        *   *Match?* Yes. "Mathematical theory" refers to the theory *of* mathematics. This aligns perfectly with "pertaining to or of the nature of mathematics."

    *   **Sense 2:** definition=relating to or having ability to think in or work with numbers | synonyms=numerical | examples=tests for rating numerical aptitude; a mathematical whiz.
        *   *Match?* No. While mathematics involves numbers, the phrase "conceptual basis of mathematical theory" is about the *subject matter* (the theory), not the *ability* of the student (the aptitude).

    *   **Sense 3:** definition=beyond question | examples=a mathematical certainty.
        *   *Match?* No. The context is about learning concepts, not about certainty.

    *   **Sense 4:** definition=statistically possible though highly improbable | examples=have a mathematical chance of making the playoffs.
        *   *Match?* No. This is a specific statistical usage, irrelevant here.

    *   **Sense 5:** definition=characterized by the exactness or precision of mathematics | examples=mathematical precision.
        *   *Match?* No. While mathematical theory is precise, the phrase is defining the *subject* (the theory), not describing its *quality* (its precision).

5.  **Conclusion:** Sense 1 is the correct fit.


[User]
Which numbered sense of "read" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: No one in his right mind actually believes that we all have an equal academic potential. -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should <t>read</t> the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline.

Senses:
1. definition=interpret something that is written or printed | examples=read the advertisement; Have you read Salman Rushdie?
2. definition=have or contain a certain wording or form | synonyms=say | examples=The passage reads as follows; What does the law say?
3. definition=look at, interpret, and say out loud something that is written or printed | examples=The King will read the proclamation at noon
4. definition=obtain data from magnetic tapes | synonyms=scan | examples=This dictionary can be read by the computer
5. definition=interpret the significance of, as of palms, tea leaves, intestines, the sky; also of human behavior | examples=She read the sky and predicted rain; I can't read his strange behavior
6. definition=interpret something in a certain way; convey a particular meaning or impression | synonyms=take | examples=I read this address as a satire; How should I take this message?
7. definition=be a student of a certain subject | synonyms=learn, study, take | examples=She is reading for the bar exam
8. definition=indicate a certain reading; of gauges and instruments | synonyms=register, show, record | examples=The thermometer showed thirteen degrees below zero; The gauge read `empty'
9. definition=audition for a stage role by reading parts of a role | examples=He is auditioning for `Julius Caesar' at Stratford this year
10. definition=to hear and understand | examples=I read you loud and clear!
11. definition=make sense of a language | synonyms=understand, interpret, translate | examples=She understands French; Can you read Greek?

reasoning_content:
1.  **Analyze the context:** The sentence containing the target word is: "Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should <t>read</t> the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator."

2.  **Determine the meaning of "read" in this context:** The subject ("Anyone who wants to appreciate...") is being advised to perform an action on "the article by Caleb Nelson... in the November American Spectator." The action is consuming the written content of the article.

3.  **Examine the senses provided:**

    *   1. definition=interpret something that is written or printed | examples=read the advertisement; Have you read Salman Rushdie? (This matches the idea of engaging with written material.)
    *   2. definition=have or contain a certain wording or form | synonyms=say | examples=The passage reads as follows; What does the law say? (Incorrect. The article itself doesn't "read" the advice.)
    *   3. definition=look at, interpret, and say out loud something that is written or printed | examples=The King will read the proclamation at noon (This is reading aloud, not necessarily the primary meaning here, though related.)
    *   4. definition=obtain data from magnetic tapes | synonyms=scan | examples=This dictionary can be read by the computer (Incorrect. Technology/data input.)
    *   5. definition=interpret the significance of, as of palms, tea leaves, intestines, the sky; also of human behavior (Incorrect. Divination.)
    *   6. definition=interpret something in a certain way; convey a particular meaning or impression | synonyms=take | examples=I read this address as a satire; How should I take this message? (Incorrect. This is about interpretation, not the physical act of consuming the text.)
    *   7. definition=be a student of a certain subject | synonyms=learn, study, take | examples=She is reading for the bar exam (Incorrect. The article is the object, not the subject of study.)
    *   8. definition=indicate a certain reading; of gauges and instruments | synonyms=register, show, record | examples=The thermometer showed thirteen degrees below zero; The gauge read `empty' (Incorrect. Instruments.)
    *   9. definition=audition for a stage role by reading parts of a role | examples=He is auditioning for `Julius Caesar' at Stratford this year (Incorrect. Acting/auditioning.)
    *   10. definition=to hear and understand | examples=I read you loud and clear! (Incorrect. This is about auditory comprehension.)
    *   11. definition=make sense of a language | synonyms=understand, interpret, translate | examples=She understands French; Can you read Greek? (Incorrect. This is about linguistic ability, not consuming a specific text.)

4.  **Match the context to the best sense:** The context requires the action of reading a published article. Sense 1 ("interpret something that is written or printed") is the most accurate and common definition for this usage.

5.  **Final check:** "Should read the article" means "should read the written content of the article." This aligns perfectly with Sense 1.


[User]
Which numbered sense of "article" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: No one in his right mind actually believes that we all have an equal academic potential. -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the <t>article</t> by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline.

Senses:
1. definition=nonfictional prose forming an independent part of a publication
2. definition=one of a class of artifacts | examples=an article of clothing
3. definition=a separate section of a legal document (as a statute or contract or will) | synonyms=clause
4. definition=(grammar) a determiner that may indicate the specificity of reference of a noun phrase

reasoning_content:
1.  **Analyze the request:** The user wants to identify which numbered sense of the word "article" (<t>article</t>) is used in the provided context. The output must be only the number.

2.  **Examine the context:** The relevant sentence is: "Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the <t>article</t> by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator."

3.  **Determine the meaning of "article" in context:**
    *   The word "article" refers to a piece of writing authored by Caleb Nelson.
    *   This piece of writing is published in a magazine/publication ("American Spectator").

4.  **Evaluate the senses:**

    *   **Sense 1:** definition=nonfictional prose forming an independent part of a publication.
        *   *Match?* Yes. A piece of writing published in a magazine is an article.

    *   **Sense 2:** definition=one of a class of artifacts | examples=an article of clothing.
        *   *Match?* No. It is not a physical object like clothing.

    *   **Sense 3:** definition=a separate section of a legal document (as a statute or contract or will) | synonyms=clause.
        *   *Match?* No. It is a journalistic piece, not a legal clause.

    *   **Sense 4:** definition=(grammar) a determiner that may indicate the specificity of reference of a noun phrase.
        *   *Match?* No. This refers to "a," "an," or "the," not the noun "article."

5.  **Conclusion:** Sense 1 is the correct meaning.

6.  **Format the output:** Return only the number.


[User]
Which numbered sense of "recent" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: No one in his right mind actually believes that we all have an equal academic potential. -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a <t>recent</t> math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline.

Senses:
1. definition=new | examples=recent graduates; a recent addition to the house
2. definition=of the immediate past or just previous to the present time | synonyms=late | examples=a late development; their late quarrel

reasoning_content:
1.  **Analyze the request:** The user wants to identify which numbered sense of the word "recent" is used in the provided context. The output must be *only* the number.

2.  **Locate the target word and context:** The target word is "recent," and the specific phrase is "himself a <t>recent</t> math major at Harvard."

3.  **Analyze the meaning of "recent" in the context:** "Recent math major" means he recently completed or is currently in the final stages of his math major at Harvard. It refers to a time frame close to the present moment (when the article was written).

4.  **Evaluate Sense 1:**
    *   Definition: new
    *   Examples: recent graduates; a recent addition to the house
    *   *Check:* While "recent graduates" is related, the core definition here is about *time* (close to now), not just "newness" in a general sense (like a new object).

5.  **Evaluate Sense 2:**
    *   Definition: of the immediate past or just previous to the present time
    *   Synonyms: late
    *   Examples: a late development; their late quarrel
    *   *Check:* A "recent math major" fits perfectly here. It means he is a student whose academic period is close to the present time.

6.  **Conclusion:** Sense 2 is the correct fit.

7.  **Format the output:** Return only the number.


[User]
Which numbered sense of "major" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: No one in his right mind actually believes that we all have an equal academic potential. -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math <t>major</t> at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline.

Senses:
1. definition=a commissioned military officer in the United States Army or Air Force or Marines; below lieutenant colonel and above captain
2. definition=British statesman who was prime minister from 1990 until 1997 (born in 1943) | synonyms=John Major, John R. Major, John Roy Major
3. definition=a university student who is studying a particular field as the principal subject | examples=she is a linguistics major
4. definition=the principal field of study of a student at a university | examples=her major is linguistics

reasoning_content:
1.  **Analyze the request:** The user wants to identify which numbered sense of the word "major" is used in the provided context. The output must be only the number.

2.  **Locate the target word in the context:** The word is "major" in the phrase: "...himself a recent math <t>major</t> at Harvard..."

3.  **Analyze the context surrounding the target word:**
    *   "Caleb Nelson (himself a recent math major at Harvard)..."
    *   "Harvard" is a university.
    *   "math" is a field of study.
    *   The structure "X (a recent Y at Z university)" suggests Y is a type of student or a field of study.

4.  **Evaluate the provided senses:**

    *   **Sense 1:** a commissioned military officer... (Irrelevant to Harvard/math).
    *   **Sense 2:** British statesman... (Irrelevant to Harvard/math).
    *   **Sense 3:** a university student who is studying a particular field as the principal subject | examples=she is a linguistics major. (Fits the context: Caleb Nelson is a student who specialized in math).
    *   **Sense 4:** the principal field of study of a student at a university | examples=her major is linguistics. (This refers to the *field* itself, not the *person*. The context says "himself a recent math major," meaning he *was* the student).

5.  **Determine the correct sense:** Since the phrase refers to Caleb Nelson (a person) who studied math at Harvard, Sense 3 ("a university student who is studying a particular field as the principal subject") is the correct fit.

6.  **Final Output Generation:** Return only the number 3.


[User]
Which numbered sense of "most" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- <t>Most</t> important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline. Study after study -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of outside interference and are governed by a powerful head.

Senses:
1. definition=used to form the superlative | synonyms=to the highest degree | examples=the king cobra is the most dangerous snake
2. definition=very | examples=a most welcome relief
3. definition=(of actions or states) slightly short of or not quite accomplished; all but | synonyms=about, almost, nearly, near, nigh, virtually | examples=the job is (just) about done; the baby was almost asleep when the alarm sounded

reasoning_content:
1.  **Analyze the request:** The user wants to identify which numbered sense of the word "most" (marked with `<t></t>`) is used in the provided context. The output must be only the number.

2.  **Locate the target word:** The target word is `<t>Most</t>` in the sentence: "Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline."

3.  **Analyze the usage in context:**
    *   The phrase is "Most important of all."
    *   "Important" is an adjective.
    *   "Most important" is the superlative form of "important."
    *   The phrase is used to rank or prioritize ideas ("Most important of all").

4.  **Evaluate the senses:**
    *   **Sense 1:** definition=used to form the superlative | synonyms=to the highest degree | examples=the king cobra is the most dangerous snake. (Matches the usage: "Most important" is a superlative.)
    *   **Sense 2:** definition=very | examples=a most welcome relief. (This is an intensifier, but the context uses it as a superlative, not just an intensifier.)
    *   **Sense 3:** definition=(of actions or states) slightly short of or not quite accomplished; all but | synonyms=about, almost, nearly, near, nigh, virtually | examples=the job is (just) about done. (This means "almost" or "nearly," which does not fit "Most important of all.")

5.  **Conclusion:** The usage "Most important of all" clearly falls under Sense 1 (forming the superlative).

6.  **Final Output Generation:** Return only the number 1.


[User]
Which numbered sense of "important" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most <t>important</t> of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline. Study after study -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of outside interference and are governed by a powerful head.

Senses:
1. definition=of great significance or value | synonyms=of import | examples=important people; the important questions of the day
2. definition=important in effect or meaning | synonyms=significant | examples=a significant change in tax laws; a significant change in the Constitution
3. definition=of extreme importance; vital to the resolution of a crisis | synonyms=crucial | examples=a crucial moment in his career; a crucial election
4. definition=having authority or ascendancy or influence | synonyms=authoritative | examples=an important official; the captain's authoritative manner
5. definition=having or suggesting a consciousness of high position | examples=recited the decree with an important air; took long important strides in the direction of his office

reasoning_content:
1.  **Analyze the target word and context:** The target word is "important," and the context is: "Most <t>important</t> of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline."

2.  **Determine the meaning of "important" in this specific sentence:** The sentence is listing desirable qualities or features for schools. The phrase "Most important of all" means that the quality being discussed (having principals with authority) is the *most significant* or *most valuable* factor among all the factors being considered (which are implied to be various aspects of school structure/operation).

3.  **Evaluate the provided senses against the determined meaning:**

    *   **Sense 1:** definition=of great significance or value | synonyms=of import | examples=important people; the important questions of the day. (This matches the idea of being highly valuable or significant.)
    *   **Sense 2:** definition=important in effect or meaning | synonyms=significant | examples=a significant change in tax laws; a significant change in the Constitution. (This also matches the idea of being highly significant, often used for data or changes.)
    *   **Sense 3:** definition=of extreme importance; vital to the resolution of a crisis | synonyms=crucial | examples=a crucial moment in his career; a crucial election. (While "most important" implies extreme importance, "crucial" usually suggests a point of crisis or necessity for survival/success, which is slightly stronger than just being the most valuable feature.)
    *   **Sense 4:** definition=having authority or ascendancy or influence | synonyms=authoritative | examples=an important official; the captain's authoritative manner. (This relates to *having* authority, not *being* the most valuable factor.)
    *   **Sense 5:** definition=having or suggesting a consciousness of high position | examples=recited the decree with an important air; took long important strides in the direction of his office. (This relates to demeanor or perceived status, not value.)

4.  **Distinguish between Sense 1 and Sense 2:**
    *   Sense 1 focuses on "great significance or value" (e.g., important questions, important people).
    *   Sense 2 focuses on "important in effect or meaning" (e.g., significant change).
    *   In the phrase "Most important of all," the speaker is ranking the *value* or *significance* of the proposed policy (having powerful principals). This aligns perfectly with Sense 1 (great significance or value). While Sense 2 is close, Sense 1 is the most direct fit for ranking the overall value of a concept or feature.

5.  **Conclusion:** Sense 1 is the best fit.


[User]
Which numbered sense of "school" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, <t>schools</t> should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline. Study after study -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of outside interference and are governed by a powerful head.

Senses:
1. definition=an educational institution | examples=the school was founded in 1900
2. definition=a building where young people receive education | synonyms=schoolhouse | examples=the school was built in 1932; he walked to school every morning
3. definition=the process of being formally educated at a school | synonyms=schooling | examples=what will you do when you finish school?
4. definition=a body of creative artists or writers or thinkers linked by a similar style or by similar teachers | examples=the Venetian school of painting
5. definition=the period of instruction in a school; the time period when school is in session | synonyms=schooltime, school day | examples=stay after school; he didn't miss a single day of school
6. definition=an educational institution's faculty and students | examples=the school keeps parents informed; the whole school turned out for the game
7. definition=a large group of fish | synonyms=shoal | examples=a school of small glittering fish swam by

reasoning_content:
1.  **Analyze the context:** The sentence containing the target word is: "Most important of all, <t>schools</t> should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline."
2.  **Analyze the surrounding text/clues:** The text discusses educational methods, textbooks, teaching methods, students, math tests, principals, faculty, and curriculum.
3.  **Determine the meaning of "schools" in this context:** The text is discussing the organizational structure and governance of educational institutions (schools) and how they should be run (having principals with authority over faculty and curriculum).
4.  **Evaluate the senses provided:**
    *   1. definition=an educational institution | examples=the school was founded in 1900 (Matches the concept of an institution.)
    *   2. definition=a building where young people receive education | synonyms=schoolhouse | examples=the school was built in 1932; he walked to school every morning (While related, the focus here is on the *institution/governance*, not just the physical building.)
    *   3. definition=the process of being formally educated at a school | synonyms=schooling | examples=what will you do when you finish school? (Refers to the process, not the institution itself.)
    *   4. definition=a body of creative artists or writers or thinkers linked by a similar style or by similar teachers | examples=the Venetian school of painting (Irrelevant.)
    *   5. definition=the period of instruction in a school; the time period when school is in session | synonyms=schooltime, school day | examples=stay after school; he didn't miss a single day of school (Refers to time, not the institution.)
    *   6. definition=an educational institution's faculty and students | examples=the school keeps parents informed; the whole school turned out for the game (This refers to the *people* within the institution, not the institution itself, although the institution contains these groups.)
    *   7. definition=a large group of fish | synonyms=shoal | examples=a school of small glittering fish swam by (Irrelevant.)
5.  **Select the best fit:** Sense 1, "an educational institution," is the most accurate definition for "schools" when discussing principals, faculty, and curriculum authority.

6.  **Final check:** The context is about the governance of educational institutions. Sense 1 is "an educational institution." This is correct.


[User]
Which numbered sense of "principal" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have <t>principals</t> with a large measure of authority over the faculty, the curriculum, and all matters of student discipline. Study after study -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of outside interference and are governed by a powerful head.

Senses:
1. definition=the original amount of a debt on which interest is calculated
2. definition=the educator who has executive authority for a school | synonyms=school principal, head teacher, head | examples=she sent unruly pupils to see the principal
3. definition=an actor who plays a principal role | synonyms=star, lead
4. definition=capital as contrasted with the income derived from it | synonyms=corpus, principal sum
5. definition=(criminal law) any person involved in a criminal offense, regardless of whether the person profits from such involvement
6. definition=the major party to a financial transaction at a stock exchange; buys and sells for his own account | synonyms=dealer

reasoning_content:
1.  **Analyze the request:** The user wants to identify which numbered sense of the word "principal" is used in the provided context. The output must be only the number.

2.  **Examine the context:** The relevant sentence is: "Most important of all, schools should have <t>principals</t> with a large measure of authority over the faculty, the curriculum, and all matters of student discipline."

3.  **Determine the meaning of "principals" in this context:** The word refers to the person in charge of the school who has authority over staff, curriculum, and discipline.

4.  **Review the provided senses:**
    *   1. original amount of a debt (Financial/Mathematical)
    *   2. the educator who has executive authority for a school | synonyms=school principal, head teacher, head | examples=she sent unruly pupils to see the principal (Educational/Authority figure)
    *   3. an actor who plays a principal role (Theatrical/Role)
    *   4. capital as contrasted with the income derived from it (Financial/Mathematical)
    *   5. (criminal law) any person involved in a criminal offense (Legal)
    *   6. the major party to a financial transaction (Financial/Stock market)

5.  **Match the context meaning to the senses:** The meaning ("person in charge of a school") perfectly matches Sense 2.

6.  **Formulate the final answer:** The correct number is 2.


[User]
Which numbered sense of "measure" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large <t>measure</t> of authority over the faculty, the curriculum, and all matters of student discipline. Study after study -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of outside interference and are governed by a powerful head.

Senses:
1. definition=any maneuver made as part of progress toward a goal | synonyms=step | examples=the situation called for strong measures; the police took steps to reduce crime
2. definition=how much there is or how many there are of something that you can quantify | synonyms=quantity, amount
3. definition=a statute in draft before it becomes law | synonyms=bill | examples=they held a public hearing on the bill
4. definition=the act or process of assigning numbers to phenomena according to a rule | synonyms=measurement, measuring, mensuration | examples=the measurements were carefully done; his mental measurings proved remarkably accurate
5. definition=a basis for comparison; a reference point against which other things can be evaluated | synonyms=standard, criterion, touchstone | examples=the schools comply with federal standards; they set the measure for all subsequent work
6. definition=(prosody) the accent in a metrical foot of verse | synonyms=meter, metre, beat, cadence
7. definition=musical notation for a repeating pattern of musical beats | synonyms=bar | examples=the orchestra omitted the last twelve bars of the song
8. definition=measuring instrument having a sequence of marks at regular intervals; used as a reference in making measurements | synonyms=measuring stick, measuring rod
9. definition=a container of some standard capacity that is used to obtain fixed amounts of a substance

reasoning_content:
1.  **Analyze the Request:** The user wants to identify which numbered sense of the word "measure" (marked with `<t>measure</t>`) is used in the provided context. The output must be only the number.

2.  **Examine the Context:** The relevant sentence is: "Most important of all, schools should have principals with a large <t>measure</t> of authority over the faculty, the curriculum, and all matters of student discipline."

3.  **Analyze the Usage:** The word "measure" is preceded by "a large" and followed by "of authority." It refers to the *degree* or *extent* of the principal's power.

4.  **Evaluate the Senses:**

    *   1. definition=any maneuver made as part of progress toward a goal | synonyms=step. (Doesn't fit "large measure of authority.")
    *   2. definition=how much there is or how many there are of something that you can quantify | synonyms=quantity, amount. (Fits perfectly. "A large measure of authority" means a large *amount* or *quantity* of authority.)
    *   3. definition=a statute in draft before it becomes law | synonyms=bill. (Irrelevant.)
    *   4. definition=the act or process of assigning numbers to phenomena according to a rule | synonyms=measurement, measuring, mensuration. (Irrelevant to authority.)
    *   5. definition=a basis for comparison; a reference point against which other things can be evaluated | synonyms=standard, criterion, touchstone. (While authority can be a standard, the phrase "large measure of authority" emphasizes the *quantity* of the power, not the standard itself.)
    *   6. definition=(prosody) the accent in a metrical foot of verse | synonyms=meter, metre, beat, cadence. (Irrelevant.)
    *   7. definition=musical notation for a repeating pattern of musical beats | synonyms=bar. (Irrelevant.)
    *   8. definition=measuring instrument having a sequence of marks at regular intervals; used as a reference in making measurements | synonyms=measuring stick, measuring rod. (Irrelevant.)
    *   9. definition=a container of some standard capacity that is used to obtain fixed amounts of a substance. (Irrelevant.)

5.  **Conclusion:** Sense 2, which relates to quantity or amount, is the correct fit for "a large measure of authority."

6.  **Final Output Generation:** Return only the number 2.


[User]
Which numbered sense of "authority" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of <t>authority</t> over the faculty, the curriculum, and all matters of student discipline. Study after study -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of outside interference and are governed by a powerful head.

Senses:
1. definition=the power or right to give orders or make decisions | synonyms=authorization, authorisation, potency, dominance, say-so | examples=he has the authority to issue warrants; deputies are given authorization to make arrests
2. definition=(usually plural) persons who exercise (administrative) control over others | examples=the authorities have issued a curfew
3. definition=an expert whose views are taken as definitive | examples=he is an authority on corporate law
4. definition=freedom from doubt; belief in yourself and your abilities | synonyms=assurance, self-assurance, confidence, self-confidence, sureness | examples=his assurance in his superiority did not make him popular; after that failure he lost his confidence
5. definition=an administrative unit of government | synonyms=agency, federal agency, government agency, bureau, office | examples=the Central Intelligence Agency; the Census Bureau
6. definition=official permission or approval | synonyms=authorization, authorisation, sanction | examples=authority for the program was renewed several times
7. definition=an authoritative written work | examples=this book is the final authority on the life of Milton

reasoning_content:
1.  **Analyze the context:** The sentence containing the target word is: "Most important of all, schools should have principals with a large measure of <t>authority</t> over the faculty, the curriculum, and all matters of student discipline."

2.  **Determine the function of "authority" in this context:** The principals are expected to have power or control *over* specific groups (faculty) and areas (curriculum, discipline). This suggests the ability to make decisions, give orders, and enforce rules.

3.  **Examine the senses provided:**

    *   1. definition=the power or right to give orders or make decisions | synonyms=authorization, authorisation, potency, dominance, say-so | examples=he has the authority to issue warrants; deputies are given authorization to make arrests
    *   2. definition=(usually plural) persons who exercise (administrative) control over others | examples=the authorities have issued a curfew (This refers to *people*, not the abstract power held by the principal.)
    *   3. definition=an expert whose views are taken as definitive | examples=he is an authority on corporate law (This refers to *knowledge/expertise*, not administrative power.)
    *   4. definition=freedom from doubt; belief in yourself and your abilities | synonyms=assurance, self-assurance, confidence, self-confidence, sureness (This refers to *confidence*, not administrative power.)
    *   5. definition=an administrative unit of government | synonyms=agency, federal agency, government agency, bureau, office (This refers to a *body/agency*, not the power held by a person.)
    *   6. definition=official permission or approval | synonyms=authorization, authorisation, sanction (While related to power, the context emphasizes the *right to govern/control* (over faculty, curriculum), not just the *permission* to do something.)
    *   7. definition=an authoritative written work | examples=this book is the final authority on the life of Milton (This refers to a *text*, not administrative power.)

4.  **Match the context to the best sense:** The principal needs the power/right to make decisions and give orders regarding the faculty and curriculum. This perfectly matches Sense 1.

5.  **Final check:** "Principals with a large measure of authority over the faculty" means they have the power/dominance to manage and direct the faculty. This aligns with Sense 1.


[User]
Which numbered sense of "faculty" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the <t>faculty</t>, the curriculum, and all matters of student discipline. Study after study -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of outside interference and are governed by a powerful head.

Senses:
1. definition=one of the inherent cognitive or perceptual powers of the mind | synonyms=mental faculty, module
2. definition=the body of teachers and administrators at a school | synonyms=staff | examples=the dean addressed the letter to the entire staff of the university

reasoning_content:
1.  **Analyze the Request:** The user wants to know which numbered sense of the word "faculty" is used in the provided context. The output must be *only* the number.

2.  **Analyze the Context:**
    *   The relevant sentence is: "Most important of all, schools should have principals with a large measure of authority over the <t>faculty</t>, the curriculum, and all matters of student discipline."
    *   The context is about school administration, principals, curriculum, and student discipline.

3.  **Analyze the Senses:**
    *   Sense 1: definition=one of the inherent cognitive or perceptual powers of the mind | synonyms=mental faculty, module. (Relates to mental ability/cognition.)
    *   Sense 2: definition=the body of teachers and administrators at a school | synonyms=staff | examples=the dean addressed the letter to the entire staff of the university. (Relates to school personnel.)

4.  **Determine the Usage:**
    *   In the phrase "authority over the faculty, the curriculum, and all matters of student discipline," "faculty" refers to the teaching staff and academic personnel of the school.
    *   This matches the definition of Sense 2.

5.  **Formulate the Output:** The correct number is 2.


[User]
Which numbered sense of "matter" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all <t>matters</t> of student discipline. Study after study -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of outside interference and are governed by a powerful head.

Senses:
1. definition=a vaguely specified concern | synonyms=affair, thing | examples=several matters to attend to; it is none of your affair
2. definition=some situation or event that is thought about | synonyms=topic, subject, issue | examples=he kept drifting off the topic; he had been thinking about the subject for several years
3. definition=that which has mass and occupies space | examples=physicists study both the nature of matter and the forces which govern it
4. definition=a problem | examples=is anything the matter?
5. definition=(used with negation) having consequence | examples=they were friends and it was no matter who won the games
6. definition=written works (especially in books or magazines) | examples=he always took some reading matter with him on the plane

reasoning_content:
1.  **Analyze the Request:** The user wants to identify which numbered sense of the word "matter" (<t>matters</t>) is used in the provided context. The output must be only the number.

2.  **Analyze the Context Sentence:** "Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all <t>matters</t> of student discipline."

3.  **Determine the Meaning of "matters" in Context:** In this sentence, "matters" refers to the various issues, concerns, or aspects related to student discipline (e.g., rules, behavior, disciplinary actions, etc.).

4.  **Evaluate the Senses:**

    *   1. definition=a vaguely specified concern | synonyms=affair, thing | examples=several matters to attend to; it is none of your affair. (Fits the idea of concerns/affairs.)
    *   2. definition=some situation or event that is thought about | synonyms=topic, subject, issue | examples=he kept drifting off the topic; he had been thinking about the subject for several years. (Fits the idea of issues/subjects.)
    *   3. definition=that which has mass and occupies space | examples=physicists study both the nature of matter and the forces which govern it. (Physical substance - Incorrect.)
    *   4. definition=a problem | examples=is anything the matter? (Too narrow; "matters" here is broader than just a single problem.)
    *   5. definition=(used with negation) having consequence | examples=they were friends and it was no matter who won the games. (Incorrect usage/context.)
    *   6. definition=written works (especially in books or magazines) | examples=he always took some reading matter with him on the plane. (Incorrect.)

5.  **Compare Senses 1 and 2:**
    *   Sense 1: "a vaguely specified concern" / "affair."
    *   Sense 2: "some situation or event that is thought about" / "topic, subject, issue."
    *   The phrase "all matters of student discipline" strongly aligns with "all issues/subjects/concerns related to student discipline." Both 1 and 2 are very close, but Sense 2 (topic, subject, issue) is perhaps the most precise fit for the administrative/educational context of "discipline." Sense 1 (affair) is also plausible.

6.  **Select the Best Fit:** Since the context refers to the scope of authority (faculty, curriculum, and *all issues* of discipline), Sense 2 ("topic, subject, issue") is the most accurate and common usage in this type of formal writing.

7.  **Final Check:** "All matters of student discipline" = "All issues/subjects of student discipline." This matches Sense 2.

8.  **Format the Output:** Return only the number.


[User]
Which numbered sense of "student" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: -- It is generally desirable to use older textbooks -- many of them, alas, out of print -- rather than newer ones. The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of <t>student</t> discipline. Study after study -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of outside interference and are governed by a powerful head.

Senses:
1. definition=a learner who is enrolled in an educational institution | synonyms=pupil, educatee
2. definition=a learned person (especially in the humanities); someone who by long study has gained mastery in one or more disciplines | synonyms=scholar, scholarly person, bookman

reasoning_content:
1.  **Analyze the Request:** The user wants to identify which numbered sense of the word "student" (<t>student</t>) is used in the provided context. The output must be *only* the number.

2.  **Analyze the Context:**
    *   The context discusses educational practices, textbooks, teaching methods ("New Math"), math tests, and school administration.
    *   The specific phrase containing the target word is: "...with students who ca not add or subtract 'learning' the conceptual basis of mathematical theory..."
    *   The word appears again in the context of school management: "...all matters of <t>student</t> discipline."

3.  **Analyze the Target Word's Usage:**
    *   In the phrase "students who ca not add or subtract...", "students" refers to people who are currently enrolled in a school and are being taught math.
    *   In the phrase "student discipline," "student" refers to the behavior and conduct of pupils in a school setting.

4.  **Analyze the Senses:**
    *   **Sense 1:** definition=a learner who is enrolled in an educational institution | synonyms=pupil, educatee. (This matches the usage in the context.)
    *   **Sense 2:** definition=a learned person (especially in the humanities); someone who by long study has gained mastery in one or more disciplines | synonyms=scholar, scholarly person, bookman. (This refers to an expert or highly educated person, which does not match the usage in the context.)

5.  **Conclusion:** The context uses "student" in the sense of an enrolled learner/pupil. This corresponds to Sense 1.

6.  **Format the Output:** Return only the number.


[User]
Which numbered sense of "study" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline. <t>Study</t> after study -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of outside interference and are governed by a powerful head. With that authority, of course, goes an unambiguous accountability.

Senses:
1. definition=a detailed critical inspection | synonyms=survey
2. definition=applying the mind to learning and understanding a subject (especially by reading) | synonyms=work | examples=mastering a second language requires a lot of work; no schools offer graduate study in interior design
3. definition=a written document describing the findings of some individual or group | synonyms=report, written report | examples=this accords with the recent study by Hill and Dale
4. definition=a state of deep mental absorption | examples=she is in a deep study
5. definition=a room used for reading and writing and studying | examples=he knocked lightly on the closed door of the study
6. definition=a branch of knowledge | synonyms=discipline, subject, subject area, subject field, field, field of study | examples=in what discipline is his doctorate?; teachers should be well trained in their subject
7. definition=preliminary drawing for later elaboration | synonyms=sketch | examples=he made several studies before starting to paint
8. definition=attentive consideration and meditation | synonyms=cogitation | examples=after much cogitation he rejected the offer
9. definition=someone who memorizes quickly and easily (as the lines for a part in a play) | examples=he is a quick study
10. definition=a composition intended to develop one aspect of the performer's technique | examples=a study in spiccato bowing

reasoning_content:
1.  **Analyze the context:** The target word is "Study" in the phrase: "<t>Study</t> after study -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of outside interference and are governed by a powerful head."

2.  **Examine the surrounding text/clues:**
    *   "Study after study" suggests a sequence of items.
    *   "the most recent from the Brookings Institution" identifies the source of these items.
    *   The Brookings Institution is a well-known think tank/research organization.
    *   The items being referenced are pieces of research or findings.

3.  **Determine the meaning of "Study" in this context:** The word refers to a piece of research, a report, or a finding produced by the institution.

4.  **Match the meaning to the provided senses:**
    *   1. detailed critical inspection (survey) - Possible, but usually refers to the *act* of inspecting.
    *   2. applying the mind to learning (work) - Incorrect.
    *   3. a written document describing the findings of some individual or group (report, written report) - This perfectly matches "the most recent from the Brookings Institution."
    *   4. state of deep mental absorption - Incorrect.
    *   5. a room - Incorrect.
    *   6. a branch of knowledge (discipline) - Incorrect.
    *   7. preliminary drawing (sketch) - Incorrect.
    *   8. attentive consideration (cogitation) - Incorrect.
    *   9. someone who memorizes quickly - Incorrect.
    *   10. a composition (musical) - Incorrect.

5.  **Conclusion:** Sense 3 is the correct meaning.


[User]
Which numbered sense of "study" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline. Study after <t>study</t> -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of outside interference and are governed by a powerful head. With that authority, of course, goes an unambiguous accountability.

Senses:
1. definition=a detailed critical inspection | synonyms=survey
2. definition=applying the mind to learning and understanding a subject (especially by reading) | synonyms=work | examples=mastering a second language requires a lot of work; no schools offer graduate study in interior design
3. definition=a written document describing the findings of some individual or group | synonyms=report, written report | examples=this accords with the recent study by Hill and Dale
4. definition=a state of deep mental absorption | examples=she is in a deep study
5. definition=a room used for reading and writing and studying | examples=he knocked lightly on the closed door of the study
6. definition=a branch of knowledge | synonyms=discipline, subject, subject area, subject field, field, field of study | examples=in what discipline is his doctorate?; teachers should be well trained in their subject
7. definition=preliminary drawing for later elaboration | synonyms=sketch | examples=he made several studies before starting to paint
8. definition=attentive consideration and meditation | synonyms=cogitation | examples=after much cogitation he rejected the offer
9. definition=someone who memorizes quickly and easily (as the lines for a part in a play) | examples=he is a quick study
10. definition=a composition intended to develop one aspect of the performer's technique | examples=a study in spiccato bowing

reasoning_content:
1.  **Analyze the context:** The sentence containing the target word is: "Study after <t>study</t> -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of outside interference and are governed by a powerful head."

2.  **Identify the target word and its usage:** The word is "Study." It is used in the phrase "Study after study," and it is immediately followed by a descriptive phrase: "the most recent from the Brookings Institution."

3.  **Determine the meaning of "Study" in this specific context:**
    *   "Brookings Institution" is a well-known think tank/research organization.
    *   When an organization publishes something, it is typically a report, paper, or research document.
    *   The phrase "Study after study" implies a sequence of these published documents.

4.  **Evaluate the provided senses against the determined meaning:**

    *   1. definition=a detailed critical inspection | synonyms=survey. (Possible, but usually refers to the *act* of inspecting, not the document itself.)
    *   2. definition=applying the mind to learning and understanding a subject... (Refers to the *process* of learning.)
    *   3. definition=a written document describing the findings of some individual or group | synonyms=report, written report | examples=this accords with the recent study by Hill and Dale. (This perfectly matches the context: a document published by the Brookings Institution.)
    *   4. definition=a state of deep mental absorption. (Incorrect.)
    *   5. definition=a room used for reading and writing and studying. (Incorrect.)
    *   6. definition=a branch of knowledge. (Incorrect.)
    *   7. definition=preliminary drawing for later elaboration. (Incorrect.)
    *   8. definition=attentive consideration and meditation. (Incorrect.)
    *   9. definition=someone who memorizes quickly and easily. (Incorrect.)
    *   10. definition=a composition intended to develop one aspect of the performer's technique. (Incorrect.)

5.  **Conclusion:** Sense 3 is the correct meaning.


[User]
Which numbered sense of "most" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline. Study after study -- the <t>most</t> recent from the Brookings Institution -- tells us that the best schools are those that are free of outside interference and are governed by a powerful head. With that authority, of course, goes an unambiguous accountability.

Senses:
1. definition=used to form the superlative | synonyms=to the highest degree | examples=the king cobra is the most dangerous snake
2. definition=very | examples=a most welcome relief
3. definition=(of actions or states) slightly short of or not quite accomplished; all but | synonyms=about, almost, nearly, near, nigh, virtually | examples=the job is (just) about done; the baby was almost asleep when the alarm sounded

reasoning_content:
1.  **Analyze the request:** The user wants to identify which numbered sense of "most" (1, 2, or 3) is used in the provided context. The output must be only the number.

2.  **Examine the context:** The target word is "most" in the phrase: "Study after study -- the <t>most</t> recent from the Brookings Institution -- tells us..."

3.  **Analyze the usage:**
    *   "the most recent" is a phrase modifying "study after study."
    *   "Recent" is an adjective.
    *   "The most recent" is the superlative form of "recent."

4.  **Evaluate the senses:**
    *   **Sense 1:** definition=used to form the superlative | synonyms=to the highest degree | examples=the king cobra is the most dangerous snake. (This matches the usage: "most recent" is the superlative of "recent.")
    *   **Sense 2:** definition=very | examples=a most welcome relief. (This is an intensifier, e.g., "most beautiful." It does not fit "most recent.")
    *   **Sense 3:** definition=(of actions or states) slightly short of or not quite accomplished; all but | synonyms=about, almost, nearly, near, nigh, virtually | examples=the job is (just) about done. (This is an approximation/nearness, e.g., "most of the people." It does not fit "most recent.")

5.  **Conclusion:** The usage "the most recent" clearly employs the superlative function, matching Sense 1.

6.  **Final Output Generation:** Return only the number 1.


[User]
Which numbered sense of "tell" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline. Study after study -- the most recent from the Brookings Institution -- <t>tells</t> us that the best schools are those that are free of outside interference and are governed by a powerful head. With that authority, of course, goes an unambiguous accountability.

Senses:
1. definition=express in words | synonyms=state, say | examples=He said that he wanted to marry her; tell me what is bothering you
2. definition=let something be known | examples=Tell them that you will be late
3. definition=narrate or give a detailed account of | synonyms=narrate, recount, recite | examples=Tell what happened; The father told a story to his child
4. definition=give instructions to or direct somebody to do something with authority | synonyms=order, enjoin, say | examples=I said to him to go home; She ordered him to do the shopping
5. definition=discern or comprehend | examples=He could tell that she was unhappy
6. definition=inform positively and with certainty and confidence | synonyms=assure | examples=I tell you that man is a crook!
7. definition=give evidence | synonyms=evidence | examples=he was telling on all his former colleague
8. definition=mark as different | synonyms=distinguish, separate, differentiate, secern, secernate, severalize | examples=We distinguish several kinds of maple

reasoning_content:
1.  **Analyze the context:** The sentence is: "Study after study -- the most recent from the Brookings Institution -- <t>tells</t> us that the best schools are those that are free of outside interference and are governed by a powerful head."
2.  **Analyze the word "tells":** In this context, "tells" refers to the findings or conclusions drawn from "Study after study."
3.  **Examine the relationship between the subject ("Study after study") and the verb ("tells"):** The studies provide information or evidence about the nature of the best schools.
4.  **Review the provided senses:**
    *   1. express in words (state, say) - Possible, but usually used for people speaking.
    *   2. let something be known - Possible, but often implies an action directed at someone.
    *   3. narrate or give a detailed account of - Focuses on storytelling, less on factual findings.
    *   4. give instructions/direct (order, enjoin) - Incorrect.
    *   5. discern or comprehend - Incorrect (the studies are doing the telling, not the reader discerning).
    *   6. inform positively and with certainty and confidence (assure) - Very strong candidate. The studies are assuring the reader of a fact.
    *   7. give evidence (synonyms=evidence) - Very strong candidate. The studies are providing evidence for the claim.
    *   8. mark as different - Incorrect.
5.  **Compare Sense 6 and Sense 7:**
    *   Sense 6: "I tell you that man is a crook!" (Focus on assurance/certainty).
    *   Sense 7: "he was telling on all his former colleague" (Focus on providing evidence/betraying).
6.  **Re-evaluate the usage:** When research or data "tells" us something, it means the data provides evidence or information that leads to a conclusion.
    *   "The studies tell us..." = "The studies provide evidence that..." (Sense 7)
    *   "The studies tell us..." = "The studies assure us that..." (Sense 6)
7.  **Determine the best fit:** While Sense 6 (inform positively) is plausible, Sense 7 (give evidence) is the most precise and common idiomatic usage when referring to research or data providing conclusions. The studies are *giving evidence* for the claim about school governance.

8.  **Final Selection:** Sense 7.


[User]
Which numbered sense of "best" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline. Study after study -- the most recent from the Brookings Institution -- tells us that the <t>best</t> schools are those that are free of outside interference and are governed by a powerful head. With that authority, of course, goes an unambiguous accountability.

Senses:
1. definition=(superlative of `good') having the most positive qualities | examples=the best film of the year; the best solution
2. definition=(comparative and superlative of `well') wiser or more advantageous and hence advisable | synonyms=better | examples=it would be better to speak to him; the White House thought it best not to respond
3. definition=having desirable or positive qualities especially those suitable for a thing specified | synonyms=good | examples=good news from the hospital; a good report card
4. definition=having the normally expected amount | synonyms=full, good | examples=gives full measure; gives good measure
5. definition=morally admirable | synonyms=good
6. definition=deserving of esteem and respect | synonyms=estimable, good, honorable, respectable | examples=all respectable companies give guarantees; ruined the family's good name
7. definition=promoting or enhancing well-being | synonyms=beneficial, good | examples=an arms limitation agreement beneficial to all countries; the beneficial effects of a temperate climate
8. definition=agreeable or pleasing | synonyms=good | examples=we all had a good time; good manners
9. definition=of moral excellence | synonyms=good, just, upright | examples=a genuinely good person; a just cause
10. definition=having or showing knowledge and skill and aptitude | synonyms=adept, expert, good, practiced, proficient, skillful | examples=adept in handicrafts; an adept juggler
11. definition=thorough | synonyms=good | examples=had a good workout; gave the house a good cleaning
12. definition=with or in a close or intimate relationship | synonyms=dear, good, near | examples=a good friend; my sisters and brothers are near and dear
13. definition=financially sound | synonyms=dependable, good, safe, secure | examples=a good investment; a secure investment
14. definition=most suitable or right for a particular purpose | synonyms=good, right, ripe | examples=a good time to plant tomatoes; the right time to act
15. definition=resulting favorably | synonyms=good, well | examples=it's a good thing that I wasn't there; it is good that you stayed
16. definition=exerting force or influence | synonyms=effective, good, in effect, in force | examples=the law is effective immediately; a warranty good for two years
17. definition=capable of pleasing | synonyms=good | examples=good looks
18. definition=appealing to the mind | synonyms=good, serious | examples=good music; a serious book
19. definition=in excellent physical condition | synonyms=good, sound | examples=good teeth; I still have one good leg
20. definition=tending to promote physical well-being; beneficial to health | synonyms=good, salutary | examples=beneficial effects of a balanced diet; a good night's sleep
21. definition=not forged | synonyms=good, honest | examples=a good dollar bill
22. definition=not left to spoil | synonyms=good, undecomposed, unspoiled, unspoilt | examples=the meat is still good
23. definition=generally admired | synonyms=good | examples=good taste

reasoning_content:
1.  **Analyze the context:** The sentence is: "Study after study -- the most recent from the Brookings Institution -- tells us that the <t>best</t> schools are those that are free of outside interference and are governed by a powerful head."
2.  **Determine the meaning of "best" in this context:** "Best schools" refers to schools that perform optimally, are most effective, or are most successful based on the studies.
3.  **Evaluate the senses provided:** I need to find the sense that aligns with "most effective/most suitable/most successful."

    *   1. definition=(superlative of `good') having the most positive qualities | examples=the best film of the year; the best solution. (This fits the idea of having the most positive qualities/being the most successful.)
    *   2. definition=(comparative and superlative of `well') wiser or more advantageous and hence advisable | synonyms=better | examples=it would be better to speak to him; the White House thought it best not to respond. (This relates to advisability, but "best schools" here refers to quality/performance, not necessarily advice.)
    *   3. definition=having desirable or positive qualities especially those suitable for a thing specified | synonyms=good | examples=good news from the hospital; a good report card. (This is a general definition of 'good', but the context uses the superlative 'best'.)
    *   14. definition=most suitable or right for a particular purpose | synonyms=good, right, ripe | examples=a good time to plant tomatoes; the right time to act. (This is a strong candidate, as the schools are deemed "best" because of their structure, making them most suitable for educational success.)

4.  **Compare Sense 1 and Sense 14:**
    *   Sense 1: "having the most positive qualities." (The schools have the most positive qualities.)
    *   Sense 14: "most suitable or right for a particular purpose." (The schools are most suitable for achieving educational goals.)

    In the context of educational studies, "best schools" usually means schools that are most effective or most successful in achieving their purpose. Both Sense 1 and Sense 14 are plausible. However, Sense 1 (superlative of 'good' having the most positive qualities) is the most direct and general interpretation of "best" when describing a high level of quality or performance. Sense 14 focuses specifically on *suitability* for a purpose, which is a specific application of quality. Since the studies are ranking schools based on overall positive outcomes (implied by the structure described), Sense 1 is the most encompassing fit for the superlative quality.

5.  **Final Selection:** Sense 1 captures the idea of having the highest level of positive qualities/performance.


[User]
Which numbered sense of "school" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline. Study after study -- the most recent from the Brookings Institution -- tells us that the best <t>schools</t> are those that are free of outside interference and are governed by a powerful head. With that authority, of course, goes an unambiguous accountability.

Senses:
1. definition=an educational institution | examples=the school was founded in 1900
2. definition=a building where young people receive education | synonyms=schoolhouse | examples=the school was built in 1932; he walked to school every morning
3. definition=the process of being formally educated at a school | synonyms=schooling | examples=what will you do when you finish school?
4. definition=a body of creative artists or writers or thinkers linked by a similar style or by similar teachers | examples=the Venetian school of painting
5. definition=the period of instruction in a school; the time period when school is in session | synonyms=schooltime, school day | examples=stay after school; he didn't miss a single day of school
6. definition=an educational institution's faculty and students | examples=the school keeps parents informed; the whole school turned out for the game
7. definition=a large group of fish | synonyms=shoal | examples=a school of small glittering fish swam by

reasoning_content:
1.  **Analyze the request:** The user wants to identify which numbered sense of the word "schools" (marked with `<t>schools</t>`) is used in the provided context. The output must be only the number.

2.  **Analyze the context:**
    *   The text discusses "New Math," "American students," "British, French, German or Japanese students," "math tests," "textbooks and teaching methods."
    *   It mentions "students who ca not add or subtract 'learning' the conceptual basis of mathematical theory."
    *   The key sentence is: "Study after study -- the most recent from the Brookings Institution -- tells us that the best <t>schools</t> are those that are free of outside interference and are governed by a powerful head."
    *   The context is discussing educational quality, governance, curriculum, and student discipline.

3.  **Evaluate the senses against the context:**

    *   **Sense 1:** definition=an educational institution | examples=the school was founded in 1900. (Matches the discussion of educational quality, governance, and institutions.)
    *   **Sense 2:** definition=a building where young people receive education | synonyms=schoolhouse | examples=the school was built in 1932; he walked to school every morning. (While related, the focus here is on the *institution* and its *governance*, not just the physical building.)
    *   **Sense 3:** definition=the process of being formally educated at a school | synonyms=schooling | examples=what will you do when you finish school? (This is the process, not the institution itself.)
    *   **Sense 4:** definition=a body of creative artists or writers or thinkers... (Irrelevant.)
    *   **Sense 5:** definition=the period of instruction in a school; the time period when school is in session | synonyms=schooltime, school day | examples=stay after school; he didn't miss a single day of school. (Irrelevant.)
    *   **Sense 6:** definition=an educational institution's faculty and students | examples=the school keeps parents informed; the whole school turned out for the game. (This refers to the collective group, but the context is discussing the *entity* that is governed by a powerful head.)
    *   **Sense 7:** definition=a large group of fish | synonyms=shoal | examples=a school of small glittering fish swam by. (Irrelevant.)

4.  **Determine the best fit:** The text is discussing the structure, quality, and governance of educational entities ("best schools are those that are free of outside interference and are governed by a powerful head"). This aligns perfectly with the definition of an educational institution.

5.  **Conclusion:** Sense 1 is the correct sense.


[User]
Which numbered sense of "outside" (marked with <t></t>) is used in the context below? Return only the number of the correct sense.

Context: The latter are modish, trendy, often downright silly, and at best insubstantial. They are based on dubious psychological and sociological theories rather than on educational experience. One of the reasons American students do so poorly in math tests, as compared with British, French, German or Japanese students, is the influence of the "New Math "on American textbooks and teaching methods. Anyone who wants to appreciate just how bizarre this situation is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article by Caleb Nelson (himself a recent math major at Harvard) in the November American Spectator. -- Most important of all, schools should have principals with a large measure of authority over the faculty, the curriculum, and all matters of student discipline. Study after study -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of <t>outside</t> interference and are governed by a powerful head. With that authority, of course, goes an unambiguous accountability.

Senses:
1. definition=relating to or being on or near the outer side or limit | examples=an outside margin
2. definition=coming from the outside | synonyms=external, extraneous | examples=extraneous light in the camera spoiled the photograph; relying upon an extraneous income
3. definition=originating or belonging beyond some bounds: | examples=the outside world; outside interests
4. definition=located, suited for, or taking place in the open air | synonyms=outdoor, out-of-door | examples=outdoor clothes; badminton and other outdoor games
5. definition=functioning outside the boundaries or precincts of an organized unit | examples=extramural hospital care and treatment; extramural studies
6. definition=leading to or from the outside | examples=an outside door
7. definition=from or between other countries | synonyms=external, international | examples=external commerce; international trade
8. definition=very unlikely | synonyms=remote | examples=an outside chance; a remote possibility
9. definition=on or toward an outer edge | examples=an outer lane; the outside lane
10. definition=(of a baseball pitch) on the far side of home plate from the batter | synonyms=away | examples=the pitch was away (or wide); an outside pitch

reasoning_content:
1.  **Analyze the context:** The sentence is: "Study after study -- the most recent from the Brookings Institution -- tells us that the best schools are those that are free of <t>outside</t> interference and are governed by a powerful head."
2.  **Determine the meaning of "outside" in this specific context:** The schools are free of "outside interference." This means the interference is coming from *outside* the school's internal operations, governance, or control.
3.  **Examine the senses provided:**
    *   1. relating to or being on or near the outer side or limit (Physical location/edge). (Unlikely)
    *   2. coming from the outside | synonyms=external, extraneous | examples=extraneous light... (Matches the idea of interference coming from an external source). (Strong candidate)
    *   3. originating or belonging beyond some bounds: | examples=the outside world; outside interests (This is broader, but "external" fits better for interference). (Possible, but 2 is more precise)
    *   4. located, suited for, or taking place in the open air (Physical location). (Incorrect)
    *   5. functioning outside the boundaries or precincts of an organized unit (Relates to activities, like extramural studies). (Possible, but 2 is a better fit for *interference*).
    *   6. leading to or from the outside (Directional). (Incorrect)
    *   7. from or between other countries (Geographical/International). (Incorrect)
    *   8. very unlikely (Adjective meaning remote). (Incorrect)
    *   9. on or toward an outer edge (Directional/Location). (Incorrect)
    *   10. (Baseball term). (Incorrect)
4.  **Compare the best candidates (2 and 3):**
    *   The phrase is "outside interference."
    *   Sense 2: "coming from the outside | synonyms=external, extraneous." This perfectly describes interference that is not internal to the school.
    *   Sense 3: "originating or belonging beyond some bounds." While technically true, Sense 2's synonym "extraneous" is the most precise fit for something unwanted or disruptive (interference) coming from an external source.
5.  **Conclusion:** Sense 2 is the most accurate definition for "outside" when referring to interference that is external to the system (the school).