[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: student
Target surface form: students
Context:
The purpose of education is to encourage young men and women to realize their full academic potential. 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 <t>students</t> 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.

Candidate senses:
1. sense_key=student%1:18:00:: | definition=a learner who is enrolled in an educational institution | synonyms=pupil, educatee
2. sense_key=student%1:18:01:: | 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

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to choose the best sense for "student" in context. The two candidate senses:

1. student%1:18:00:: | definition=a learner who is enrolled in an educational institution | synonyms=pupil, educatee
2. student%1:18:01:: | 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

Context: Discusses education, textbooks, math tests, comparing American students with British, French, German, Japanese students. It mentions "students who ca not add or subtract 'learning' the conceptual basis of mathematical theory". Clearly referring to students as pupils in school, not as learned scholars. The context talks about American students doing poorly in math tests, which refers to learners enrolled in educational institutions. So sense 1 is correct.

Return JSON: {"sense_index": 1}


attempt_kind: initial

status: success

[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: so
Target surface form: so
Context:
The purpose of education is to encourage young men and women to realize their full academic potential. 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 <t>so</t> 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.

Candidate senses:
1. sense_key=so%4:02:02:: | definition=to a very great extent or degree | examples=the idea is so obvious; never been so happy
2. sense_key=so%4:02:06:: | definition=in a manner that facilitates | examples=he observed the snakes so he could describe their behavior; he stooped down so he could pick up his hat
3. sense_key=so%4:02:05:: | definition=in such a condition or manner, especially as expressed or implied | examples=They're happy and I hope they will remain so; so live your life that old age will bring no regrets
4. sense_key=so%4:02:07:: | definition=to a certain unspecified extent or degree | examples=I can only go so far with this student; can do only so much in a day
5. sense_key=so%4:02:08:: | definition=in the same way; also | examples=I was offended and so was he; worked hard and so did she
6. sense_key=so%4:02:04:: | definition=in the way indicated; ; ; (`thusly' is a nonstandard variant) | synonyms=thus, thusly | examples=hold the brush so; set up the pieces thus
7. sense_key=so%4:02:03:: | definition=(usually followed by `that') to an extent or degree as expressed | examples=he was so tired he could hardly stand; so dirty that it smells
8. sense_key=so%4:02:09:: | definition=subsequently or soon afterward (often used as sentence connectors) | synonyms=then, and so, and then | examples=then he left; go left first, then right
9. sense_key=so%4:02:10:: | definition=(used to introduce a logical conclusion) from that fact or reason or as a result | synonyms=therefore, hence, thence, thus | examples=therefore X must be true; the eggs were fresh and hence satisfactory
10. sense_key=so%4:02:00:: | definition=in truth (often tends to intensify) | synonyms=indeed | examples=they said the car would break down and indeed it did; it is very cold indeed

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

finish_reason: stop

role: assistant

reasoning_content:
We are asked: "Choose the single best indexed sense." The target is "so" in: "One of the reasons American students do so poorly in math tests..." The sense candidates are numbered 1 to 10. We need to return only a JSON object with the sense_index.

Let's analyze the context: "do so poorly in math tests" means to perform very poorly, to a great extent. The "so" here is an intensifier meaning "to a very great extent or degree." That matches sense 1: "to a very great extent or degree", examples: "the idea is so obvious; never been so happy". The context says "do so poorly", which is exactly like "so poorly" meaning very poorly. So sense 1 seems correct.

Check other senses:
2: "in a manner that facilitates" - no, it's not about facilitating.
3: "in such a condition or manner" - could be, but it's more like "remain so" meaning in that condition. But here "do so poorly" is not "do in such a condition" but "do to such an extent." Sense 3 is more about a state: "remain so", that doesn't fit.
4: "to a certain unspecified extent or degree" - "I can only go so far" - that implies a limited extent. Here it's not unspecified; it's emphatic.
5: "in the same way; also" - no.
6: "in the way indicated" - "hold the brush so" - no.
7: "usually followed by 'that'..." - "so tired that he could hardly stand" - here there is no 'that' clause, just "so poorly". But sense 7 often has an explicit or implied result clause. In the sentence, it's just "do so poorly", no result clause. So not 7.
8: "subsequently or soon afterward" - no.
9: "therefore" - no.
10: "in truth (often tends to intensify)" - "indeed" - it is an intensifier, but sense 10 is like "it is very cold indeed" where "indeed" emphasizes the truth. But "so" in "so poorly" is a degree intensifier, not a truth intensifier like "indeed". Sense 1 is explicitly "to a very great extent or degree", which fits.

Thus, sense 1 is the best match.

Answer: {"sense_index": 1}

format: unknown

native_finish_reason: stop

provider: Novita

currency: USD


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: compare
Target surface form: compared
Context:
The purpose of education is to encourage young men and women to realize their full academic potential. 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 <t>compared</t> 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.

Candidate senses:
1. sense_key=compare%2:31:00:: | definition=examine and note the similarities or differences of | examples=John compared his haircut to his friend's; We compared notes after we had both seen the movie
2. sense_key=compare%2:42:00:: | definition=be comparable | examples=This car does not compare with our line of Mercedes
3. sense_key=compare%2:31:01:: | definition=consider or describe as similar, equal, or analogous | synonyms=liken, equate | examples=We can compare the Han dynasty to the Romans; You cannot equate success in financial matters with greed
4. sense_key=compare%2:32:00:: | definition=to form the comparative or superlative form on an adjective or adverb

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to disambiguate the word "compared" in the given context. The target lemma is "compare", and the surface form is "compared". The context is: "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." Here, "compared" is used in a passive-like construction: "as compared with" means when comparing American students with students from other countries. The phrase "as compared with" typically means "in comparison with". Which sense fits best?

Let's look at the candidate senses:
1. examine and note the similarities or differences of (examples: John compared his haircut to his friend's; We compared notes...) This sense involves actively examining similarities and differences. In the context, it's not about someone actively examining; it's a passive comparison of performance.
2. be comparable (examples: This car does not compare with our line of Mercedes) This sense is about being of equal quality or being worthy of comparison. It's often used in negative or questions. "as compared with" might be a fixed phrase, but the sense is that American students do poorly in comparison to others, not that they are comparable.
3. consider or describe as similar, equal, or analogous (synonyms: liken, equate; examples: We can compare the Han dynasty to the Romans; You cannot equate success in financial matters with greed) This is about equating things, which doesn't fit because we're not saying American students are similar to others; we're contrasting performance.
4. to form the comparative or superlative form on an adjective or adverb (linguistic sense, not relevant).

Now, "as compared with" is a phrase meaning "in comparison with". It's used to introduce a standard of comparison. Which WordNet sense covers this? Usually, "compare" in this kind of construction might be sense 2 (be comparable) but that sense is intransitive: "This car does not compare with..." Meaning "This car is not comparable to..." In our sentence, we have "do so poorly ... as compared with ..." This is like "do so poorly when compared with", which is a passive use of sense 1: examine and note the differences. Specifically, if we say "X does poorly as compared with Y", it means "when X is compared with Y (i.e., when one examines the differences), X does poorly." So it's sense 1 used in a passive construction. The examples for sense 1 include "We compared notes", which is active examination. But the passive "compared" is just the past participle of that sense.

Sense 2 is intransitive, meaning "to be comparable". "A compares with B" means A is as good as B. In our sentence, "as compared with" is not "as A compares with B". It's a fixed phrase. If we rephrase: "American students do poorly, as they are compared with British students" -> that means when someone compares them, they do poorly. So it's sense 1.

Let's check: In WordNet, sense 1 is the basic comparison sense. The phrase "compared with" is often an adverbial phrase meaning "in comparison with", which is derived from sense 1. So sense 1 is the correct one.

But we must return the index of the chosen sense. The indices are given: 1, 2, 3, 4. We choose sense 1.

Thus, the answer is {"sense_index": 1}.

provider: SiliconFlow


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: student
Target surface form: students
Context:
The purpose of education is to encourage young men and women to realize their full academic potential. 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 <t>students</t>, 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.

Candidate senses:
1. sense_key=student%1:18:00:: | definition=a learner who is enrolled in an educational institution | synonyms=pupil, educatee
2. sense_key=student%1:18:01:: | 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

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to disambiguate "students" in the given context. The two candidate senses are:

1. student%1:18:00:: - a learner who is enrolled in an educational institution. Synonyms: pupil, educatee.
2. student%1:18:01:: - 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.

The context discusses education, comparing American students' math performance to British, French, German, or Japanese students. It mentions "students who can't add or subtract" and "learning the conceptual basis of mathematical theory." The focus is on students in educational institutions, specifically in math tests and classrooms. The target "students" refers to learners enrolled in schools, not accomplished scholars. Thus, sense 1 is clearly the correct one.

The answer should be a JSON object with the sense_index. Since the senses are indexed 1 and 2, we choose 1.

Final output: {"sense_index": 1}

provider: WandB


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: influence
Target surface form: influence
Context:
The purpose of education is to encourage young men and women to realize their full academic potential. 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 <t>influence</t> 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.

Candidate senses:
1. sense_key=influence%1:07:00:: | definition=a power to affect persons or events especially power based on prestige etc | examples=used her parents' influence to get the job
2. sense_key=influence%1:04:00:: | definition=causing something without any direct or apparent effort
3. sense_key=influence%1:09:00:: | definition=a cognitive factor that tends to have an effect on what you do | examples=her wishes had a great influence on his thinking
4. sense_key=influence%1:19:00:: | definition=the effect of one thing (or person) on another | examples=the influence of mechanical action
5. sense_key=influence%1:18:00:: | definition=one having power to influence another | examples=she was the most important influence in my life; he was a bad influence on the children

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given the target word "influence" with its context and several senses. The context is discussing education, textbooks, and specifically the "New Math" influence on American textbooks and teaching methods, which is cited as a reason for poor math performance. The phrase is: "the <t>influence</t> of the 'New Math' on American textbooks and teaching methods." So, we need to select the most appropriate WordNet sense.

Let's examine each candidate sense:

1. sense_key=influence%1:07:00:: | definition=a power to affect persons or events especially power based on prestige etc | examples=used her parents' influence to get the job
2. sense_key=influence%1:04:00:: | definition=causing something without any direct or apparent effort
3. sense_key=influence%1:09:00:: | definition=a cognitive factor that tends to have an effect on what you do | examples=her wishes had a great influence on his thinking
4. sense_key=influence%1:19:00:: | definition=the effect of one thing (or person) on another | examples=the influence of mechanical action
5. sense_key=influence%1:18:00:: | definition=one having power to influence another | examples=she was the most important influence in my life; he was a bad influence on the children

Now, "influence" in this context is about the "New Math" having an effect on textbooks and teaching methods. It's about the effect or power that one thing (New Math) has on another (textbooks and methods). Sense 1 is about power to affect, especially based on prestige. Sense 2 is about causing something without direct effort. Sense 3 is a cognitive factor affecting behavior. Sense 4 is the effect of one thing on another. Sense 5 is a person or thing that has power to influence.

Our context: "the influence of the 'New Math' on American textbooks and teaching methods." This clearly refers to the effect that the New Math had on these things. It's not about power based on prestige, nor a cognitive factor, nor an influential person or thing (sense 5 is a count noun, e.g., "she was an influence"). It's about the effect itself. So sense 4 ("the effect of one thing (or person) on another") fits perfectly. The example given for sense 4 is "the influence of mechanical action," which is a similar structure: the effect of A on B.

Thus, the best sense is 4.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: american
Target surface form: American
Context:
The purpose of education is to encourage young men and women to realize their full academic potential. 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 <t>American</t> 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.

Candidate senses:
1. sense_key=american%3:01:01:: | definition=of or relating to the United States of America or its people or language or culture | examples=American citizens; American English
2. sense_key=american%3:01:00:: | definition=of or relating to or characteristic of the continents and islands of the Americas | examples=the American hemisphere; American flora and fauna

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content: We are asked: "Target lemma: american ... Target surface form: American ... Context ... Choose the single best indexed sense." The context is about American students, American textbooks, and the American Spectator. Clearly this is referring to the United States, not the broader Americas. Sense 1 is "of or relating to the United States of America", sense 2 is "relating to the continents and islands of the Americas". The context is clearly about the US, so sense 1 is correct. Return {"sense_index": 1}.

provider: StreamLake


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: want
Target surface form: wants
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 <t>wants</t> 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.

Candidate senses:
1. sense_key=want%2:37:00:: | definition=feel or have a desire for; want strongly | synonyms=desire | examples=I want to go home now; I want my own room
2. sense_key=want%2:34:00:: | definition=have need of | synonyms=need, require | examples=This piano wants the attention of a competent tuner
3. sense_key=want%2:35:00:: | definition=hunt or look for; want for a particular reason | examples=Your former neighbor is wanted by the FBI; Uncle Sam wants you
4. sense_key=want%2:31:01:: | definition=wish or demand the presence of | examples=I want you here at noon!
5. sense_key=want%2:42:01:: | definition=be without, lack; be deficient in | examples=want courtesy; want the strength to go on living

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We need to disambiguate "wants" (lemma want) in the given context. The sentence: "Anyone who <t>wants</t> to appreciate just how bizarre this situation is ... should read the article..." Here "wants" is a form of "want". The context is about someone having a desire to appreciate something, so it's a desire to do something. That aligns with sense 1: feel or have a desire for; want strongly. The example: "I want to go home now; I want my own room". The structure "wants to appreciate" matches that. Sense 2 is about needing something (This piano wants the attention...). Sense 3 is about being hunted/looked for (wanted by FBI). Sense 4 is about demanding presence (I want you here). Sense 5 is about lacking (want courtesy). None of those fit. So sense 1 is correct.

Thus, output {"sense_index": 1}.

provider: Wafer


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: appreciate
Target surface form: appreciate
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 <t>appreciate</t> 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.

Candidate senses:
1. sense_key=appreciate%2:37:00:: | definition=recognize with gratitude; be grateful for
2. sense_key=appreciate%2:31:00:: | definition=be fully aware of; realize fully | synonyms=take account | examples=Do you appreciate the full meaning of this letter?
3. sense_key=appreciate%2:40:00:: | definition=hold dear | synonyms=prize, value, treasure | examples=I prize these old photographs
4. sense_key=appreciate%2:30:00:: | definition=gain in value | synonyms=apprize, apprise, revalue | examples=The yen appreciated again!
5. sense_key=appreciate%2:30:01:: | definition=increase the value of | synonyms=apprize, apprise | examples=The Germans want to appreciate the Deutsche Mark

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given a target lemma "appreciate" in context: "Anyone who wants to <t>appreciate</t> just how bizarre this situation is ... should read the article..."

The context is about understanding or realizing how bizarre the situation is. The word "appreciate" here means to fully realize or be aware of something. Let's examine the candidate senses:

1. sense_key=appreciate%2:37:00:: | definition=recognize with gratitude; be grateful for
   - This is about gratitude, not about understanding.

2. sense_key=appreciate%2:31:00:: | definition=be fully aware of; realize fully | synonyms=take account | examples=Do you appreciate the full meaning of this letter?
   - This matches: "appreciate just how bizarre" means realize fully how bizarre.

3. sense_key=appreciate%2:40:00:: | definition=hold dear | synonyms=prize, value, treasure | examples=I prize these old photographs
   - This is about valuing something, not about understanding.

4. sense_key=appreciate%2:30:00:: | definition=gain in value | synonyms=apprize, apprise, revalue | examples=The yen appreciated again!
   - Financial sense, not fitting.

5. sense_key=appreciate%2:30:01:: | definition=increase the value of | synonyms=apprize, apprise | examples=The Germans want to appreciate the Deutsche Mark
   - Also financial, not fitting.

Clearly, sense 2 is the correct one. So we output {"sense_index": 2}.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: just
Target surface form: just
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 <t>just</t> 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.

Candidate senses:
1. sense_key=just%4:02:00:: | definition=and nothing more | synonyms=merely, simply, only, but | examples=I was merely asking; it is simply a matter of time
2. sense_key=just%4:02:05:: | definition=indicating exactness or preciseness | synonyms=precisely, exactly | examples=he was doing precisely (or exactly) what she had told him to do; it was just as he said--the jewel was gone
3. sense_key=just%4:02:01:: | definition=only a moment ago | synonyms=just now | examples=he has just arrived; the sun just now came out
4. sense_key=just%4:02:03:: | definition=absolutely | synonyms=simply | examples=I just can't take it anymore; he was just grand as Romeo
5. sense_key=just%4:02:04:: | definition=only a very short time before; ; ; ; ; - W.B.Yeats | synonyms=barely, hardly, scarcely, scarce | examples=they could barely hear the speaker; we hardly knew them
6. sense_key=just%4:02:06:: | definition=exactly at this moment or the moment described | examples=we've just finished painting the walls, so don't touch them

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given the target lemma "just" and the surface form "just". The context is: "Anyone who wants to appreciate <t>just</t> how bizarre this situation is ... should read the article ..." In this sentence, "just" modifies "how bizarre this situation is". It means "exactly" or "precisely" how bizarre. It is emphasizing the degree of bizarreness, indicating exactness. Let's look at the candidate senses.

Sense 1: "and nothing more" (merely, simply) – This doesn't fit because it's not reducing the meaning to "only" but rather intensifying "how bizarre".

Sense 2: "indicating exactness or preciseness" (precisely, exactly) – This fits: "just how bizarre" means "exactly how bizarre". Examples: "it was just as he said" – similar structure.

Sense 3: "only a moment ago" – temporal, not applicable.

Sense 4: "absolutely" (simply) – Could be a candidate if meaning "absolutely" as intensifier: "I just can't take it anymore" emphasizes the degree. But in the phrase "just how bizarre", it's more about exactness than absolute emphasis. The example "he was just grand as Romeo" is a different usage. In our context, it's "just how bizarre", which is closer to "exactly".

Sense 5: "only a very short time before" (barely, hardly) – Not applicable.

Sense 6: "exactly at this moment or the moment described" – Temporal, not applicable.

So Sense 2 is the best match: indicating exactness, with synonyms precisely, exactly. The phrase "just how bizarre" means "exactly how bizarre". So the answer is sense 2.

Now, output JSON: {"sense_index": 2}

provider: Baidu


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: situation
Target surface form: situation
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 <t>situation</t> 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.

Candidate senses:
1. sense_key=situation%1:26:00:: | definition=the general state of things; the combination of circumstances at a given time; ; ; - Franklin D.Roosevelt | synonyms=state of affairs | examples=the present international situation is dangerous; wondered how such a state of affairs had come about
2. sense_key=situation%1:26:01:: | definition=a condition or position in which you find yourself | synonyms=position | examples=the unpleasant situation (or position) of having to choose between two evils; found herself in a very fortunate situation
3. sense_key=situation%1:26:02:: | definition=a complex or critical or unusual difficulty | examples=the dangerous situation developed suddenly; that's quite a situation
4. sense_key=situation%1:15:00:: | definition=physical position in relation to the surroundings | synonyms=site | examples=the sites are determined by highly specific sequences of nucleotides
5. sense_key=situation%1:04:00:: | definition=a job in an organization | synonyms=position, post, berth, office, spot, billet | examples=he occupied a post in the treasury

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given a sentence with the target word "situation". The context discusses how bizarre a certain educational situation is, where students who can't add or subtract are learning the conceptual basis of mathematical theory. We need to choose the best sense from the provided candidates.

Let's analyze the context:
"Anyone who wants to appreciate just how bizarre this <t>situation</t> is -- with students who ca not add or subtract "learning "the conceptual basis of mathematical theory -- should read the article..."

Here, "situation" refers to the set of circumstances or the state of affairs in education, specifically the influence of "New Math" on textbooks and teaching methods that leads to students learning conceptual theory without basic skills. It's not about a personal condition (sense 2), not a difficulty in the sense of a crisis (sense 3), not a physical position (sense 4), and not a job (sense 5). It's a general state of things, a combination of circumstances. Sense 1 is "the general state of things; the combination of circumstances at a given time", which fits perfectly. The example: "the present international situation is dangerous" shows a similar broad usage. Sense 2 is more about a personal condition (e.g., finding oneself in a fortunate situation), but here it's a bizarre situation in education, a state of affairs. Sense 3 is about a difficulty, but the emphasis is on the state of affairs, not just a problem. However, "situation" can sometimes mean a complex difficulty. Let's compare: Sense 1 definition: "the general state of things; the combination of circumstances at a given time". Sense 3: "a complex or critical or unusual difficulty". The context mentions "bizarre" which suggests unusual, but it's describing the whole state of math education, not just a difficulty. The phrase "this situation" points to the overall set of circumstances described earlier: the use of modish textbooks, dubious theories, the influence of New Math, resulting in students who can't add yet learn theory. That's a state of affairs. So sense 1 is most appropriate.

Thus, the answer is sense index 1.

provider: DeepInfra


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: student
Target surface form: students
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 <t>students</t> 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.

Candidate senses:
1. sense_key=student%1:18:00:: | definition=a learner who is enrolled in an educational institution | synonyms=pupil, educatee
2. sense_key=student%1:18:01:: | 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

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content: We are asked to do word sense disambiguation for the target word "students" in the given context. The target surface form is "students", which is plural of "student". The two candidate senses are provided: sense 1: "a learner who is enrolled in an educational institution" (pupil, educatee); sense 2: "a learned person... scholar". The context is about American students performing poorly in math tests, comparing them to British, French, German or Japanese students. The sentence: "One of the reasons American students do so poorly in math tests..." clearly refers to students as learners in educational institutions (schools). There is no indication they are scholars or learned persons. So sense 1 is the correct one. The instruction: return JSON with sense_index, so 1.

provider: Alibaba


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: add
Target surface form: add
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 <t>add</t> 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.

Candidate senses:
1. sense_key=add%2:30:00:: | definition=make an addition (to); join or combine or unite with others; increase the quality, quantity, size or scope of | examples=We added two students to that dorm room; She added a personal note to her letter
2. sense_key=add%2:32:01:: | definition=state or say further | synonyms=append, supply | examples=`It doesn't matter,' he supplied
3. sense_key=add%2:40:00:: | definition=bestow a quality on | synonyms=lend, impart, bestow, contribute, bring | examples=Her presence lends a certain cachet to the company; The music added a lot to the play
4. sense_key=add%2:31:00:: | definition=make an addition by combining numbers | synonyms=add together | examples=Add 27 and 49, please!
5. sense_key=add%2:32:00:: | definition=determine the sum of | synonyms=total, tot, tot up, sum, sum up, summate | examples=Add all the people in this town to those of the neighboring town
6. sense_key=add%2:42:00:: | definition=constitute an addition | examples=This paper will add to her reputation

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to choose the best sense for "add" in the context: "students who ca not add or subtract". The options are various WordNet senses. Let's examine the context: "students who ca not add or subtract 'learning' the conceptual basis of mathematical theory". The phrase "add or subtract" clearly refers to basic arithmetic operations: performing addition and subtraction. So the sense is mathematical: performing the operation of addition. Looking at the candidate senses:

1. general addition: make an addition, join or combine, etc. Not specific to arithmetic.
2. state or say further. Not relevant.
3. bestow a quality. Not relevant.
4. make an addition by combining numbers. Examples: Add 27 and 49, please! This is exactly arithmetic: adding numbers.
5. determine the sum of. Similar to 4, but with synonyms like total, sum up. Example: Add all the people... This also involves arithmetic but in a broader sense (summing a set). However, the context talks about students who can't add or subtract, which is basic arithmetic. Sense 4 is specifically "make an addition by combining numbers" and example "Add 27 and 49, please!" fits the simple skill. Sense 5 is about determining the sum, which might be seen as a slightly different nuance, but both are close. Which is the primary sense for simple arithmetic? WordNet often distinguishes between a verb of adding numbers (sense 4) and summing (sense 5). The context "add or subtract" pairs add with subtract. Subtract is an arithmetic operation. In WordNet, "add" sense 4 is the one that directly contrasts with subtract. Sense 5 is often used when totaling up a list. So sense 4 seems best. Moreover, the example for sense 4 is "Add 27 and 49, please!" which is a classic elementary math problem. So I'll go with sense 4.

Thus, answer: {"sense_index": 4}.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: subtract
Target surface form: subtract
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 <t>subtract</t> "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.

Candidate senses:
1. sense_key=subtract%2:31:00:: | definition=make a subtraction | synonyms=deduct, take off | examples=subtract this amount from my paycheck
2. sense_key=subtract%2:30:00:: | definition=take off or away | examples=this prefix was subtracted when the word was borrowed from French

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to perform word sense disambiguation for the word "subtract" in the given context. The context includes the phrase "students who cannot add or subtract" in the context of math tests. The target word is in angle brackets: <t>subtract</t>.

Two candidate senses:
1. sense_key=subtract%2:31:00:: | definition=make a subtraction | synonyms=deduct, take off | examples=subtract this amount from my paycheck
2. sense_key=subtract%2:30:00:: | definition=take off or away | examples=this prefix was subtracted when the word was borrowed from French

We need to choose the best sense. The context is about math: "students who cannot add or subtract" and "learning the conceptual basis of mathematical theory". So "subtract" here clearly refers to the arithmetic operation of subtraction. Sense 1 is "make a subtraction" with synonyms deduct, take off, and an example about subtracting from a paycheck, which is a mathematical operation. Sense 2 is more general: "take off or away" with a linguistic example about a prefix being subtracted. In the context of math, sense 1 is the correct one.

Thus, the best indexed sense is 1.

Return JSON: {"sense_index": 1}

provider: Parasail


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: learn
Target surface form: learning
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.

Candidate senses:
1. sense_key=learn%2:31:00:: | definition=gain knowledge or skills | synonyms=larn, acquire | examples=She learned dancing from her sister; I learned Sanskrit
2. sense_key=learn%2:31:01:: | 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. sense_key=learn%2:31:03:: | definition=commit to memory; learn by heart | synonyms=memorize, memorise, con | examples=Have you memorized your lines for the play yet?
4. sense_key=learn%2:31:02:: | definition=be a student of a certain subject | synonyms=study, read, take | examples=She is reading for the bar exam
5. sense_key=learn%2:32:00:: | definition=impart skills or knowledge to | synonyms=teach, instruct | examples=I taught them French; He instructed me in building a boat
6. sense_key=learn%2:32:02:: | 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

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given the context: "...with students who ca not add or subtract '<t>learning</t>' the conceptual basis of mathematical theory..." The target word is "learning" (lemma "learn", surface form "learning"). The context is about students who can't add or subtract, but are "learning" the conceptual basis of mathematical theory. This is criticizing the "New Math" approach where students are taught abstract concepts rather than basic arithmetic. So "learning" here means acquiring knowledge or skills, specifically they are being taught or are studying the conceptual basis. It's not accidental discovery (sense 2), not memorization (sense 3), not studying a specific subject like a course (sense 4 is "be a student of a certain subject" but that sense is more about taking a course or being a student, like "She is reading for the bar exam" – that's studying law). Sense 4: "be a student of a certain subject; study, read, take". Example: "She is reading for the bar exam." This implies a formal course of study. However, in the context, "learning the conceptual basis" is more about gaining knowledge or skills, not necessarily being a student of a subject. The phrase "learning the conceptual basis" is similar to "acquiring knowledge about the conceptual basis". Sense 1: "gain knowledge or skills" is broad. Sense 4 is more specific to being enrolled or dedicating oneself to a subject. The context says "students who can't add or subtract 'learning' the conceptual basis" – they are currently "learning" it. The word "learning" here is a gerund, meaning the process of gaining knowledge. It fits sense 1 perfectly. Sense 4 might also fit, but sense 1 is more general and directly means acquiring knowledge. Sense 4 implies a deliberate course of study, but the example "She is reading for the bar exam" shows that sense is used for a specific qualification or subject of study. The context doesn't mention any specific course; it's just the act of learning conceptual basis. So sense 1 is the best.

Sense 5 is "teach", but "learning" is not used that way in modern English; though "learn" can mean "teach" in nonstandard dialects, but here it's clearly the students learning, not teaching. Sense 6 is about finding out with certainty, not applicable.

Thus, sense_index 1.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: basis
Target surface form: basis
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.

Candidate senses:
1. sense_key=basis%1:24:00:: | 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. sense_key=basis%1:09:00:: | 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. sense_key=basis%1:24:01:: | definition=the most important or necessary part of something | synonyms=base | examples=the basis of this drink is orange juice

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given a target lemma "basis" and its surface form "basis" in a context. The context is a paragraph discussing textbooks, education, and math teaching. The sentence containing the target is: "...with students who can not add or subtract 'learning' the conceptual <t>basis</t> of mathematical theory..."

We have three candidate senses:

1. sense_key=basis%1:24:00:: 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. sense_key=basis%1:09:00:: 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. sense_key=basis%1:24:01:: definition: the most important or necessary part of something; synonyms: base; examples: "the basis of this drink is orange juice".

We need to disambiguate based on the context.

The target phrase: "learning the conceptual basis of mathematical theory". Here "basis" refers to the foundational ideas or fundamental assumptions of mathematical theory. It's about the conceptual underpinnings, not about a footing or relationship (sense 1) nor about a main ingredient (sense 3). Sense 2 specifically defines "the fundamental assumptions from which something is begun or developed or calculated or explained". This aligns well with "conceptual basis of mathematical theory". In mathematics, the basis of a theory refers to its axioms, fundamental assumptions, or foundational concepts. The example in sense 2: "the whole argument rested on a basis of conjecture" also fits the idea of foundational assumptions. Sense 1 is more about a footing or status in a social/professional relationship, like "working on a temporary basis". Sense 3 is about the main ingredient or core component of something, like a drink's base. So sense 2 is clearly the best.

Thus, return {"sense_index": 2}.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: mathematical
Target surface form: mathematical
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.

Candidate senses:
1. sense_key=mathematical%3:01:00:: | definition=of or pertaining to or of the nature of mathematics | examples=a mathematical textbook; slide rules and other mathematical instruments
2. sense_key=mathematical%3:00:00:: | 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. sense_key=mathematical%5:00:00:unquestionable:00 | definition=beyond question | examples=a mathematical certainty
4. sense_key=mathematical%5:00:00:possible:00 | definition=statistically possible though highly improbable | examples=have a mathematical chance of making the playoffs
5. sense_key=mathematical%5:00:00:exact:00 | definition=characterized by the exactness or precision of mathematics | examples=mathematical precision

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to disambiguate the target word "mathematical" in the context. The target is in the phrase: "the conceptual basis of mathematical theory". Let's look at the context: The passage talks about "New Math" and American students doing poorly in math tests. It mentions "the conceptual basis of mathematical theory" in quotes, indicating it's a concept from math education. So, "mathematical theory" here refers to theories about mathematics, like set theory, etc. The sense should be about pertaining to mathematics as a field. Looking at the candidate senses:

1. "of or pertaining to or of the nature of mathematics" - this fits: "mathematical theory" means theory of mathematics.
2. "relating to or having ability to think in or work with numbers" - this is about numerical aptitude, not about the theory.
3. "beyond question" - not applicable.
4. "statistically possible though highly improbable" - not applicable.
5. "characterized by the exactness or precision of mathematics" - this could potentially apply if we talk about precision, but the phrase is "mathematical theory", not "mathematical precision". It's not about exactness here, it's about the theory itself.

So the best fit is sense 1.

Thus, the answer is {"sense_index": 1}.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: read
Target surface form: read
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.

Candidate senses:
1. sense_key=read%2:31:00:: | definition=interpret something that is written or printed | examples=read the advertisement; Have you read Salman Rushdie?
2. sense_key=read%2:42:00:: | definition=have or contain a certain wording or form | synonyms=say | examples=The passage reads as follows; What does the law say?
3. sense_key=read%2:31:01:: | definition=look at, interpret, and say out loud something that is written or printed | examples=The King will read the proclamation at noon
4. sense_key=read%2:31:06:: | definition=obtain data from magnetic tapes | synonyms=scan | examples=This dictionary can be read by the computer
5. sense_key=read%2:31:02:: | 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. sense_key=read%2:31:09:: | 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. sense_key=read%2:31:05:: | definition=be a student of a certain subject | synonyms=learn, study, take | examples=She is reading for the bar exam
8. sense_key=read%2:32:02:: | 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. sense_key=read%2:36:05:: | definition=audition for a stage role by reading parts of a role | examples=He is auditioning for `Julius Caesar' at Stratford this year
10. sense_key=read%2:31:08:: | definition=to hear and understand | examples=I read you loud and clear!
11. sense_key=read%2:31:04:: | definition=make sense of a language | synonyms=understand, interpret, translate | examples=She understands French; Can you read Greek?

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to disambiguate the word "read" in the context: "... should <t>read</t> the article by Caleb Nelson ...". This is clearly about reading an article, so it's the most basic sense of interpreting written text. The candidate senses:
1. interpret something that is written or printed (e.g., read the advertisement)
3. look at, interpret, and say out loud something that is written or printed (reading a proclamation aloud)
In context, it's simply reading an article, not necessarily aloud. So sense 1 is the best. Sense 3 involves reading aloud, which isn't indicated. So answer: {"sense_index": 1}.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: article
Target surface form: article
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.

Candidate senses:
1. sense_key=article%1:10:00:: | definition=nonfictional prose forming an independent part of a publication
2. sense_key=article%1:03:00:: | definition=one of a class of artifacts | examples=an article of clothing
3. sense_key=article%1:10:02:: | definition=a separate section of a legal document (as a statute or contract or will) | synonyms=clause
4. sense_key=article%1:10:01:: | definition=(grammar) a determiner that may indicate the specificity of reference of a noun phrase

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to choose the best word sense for "article" in the context. The target lemma is "article" and surface form is "article". The context mentions: "should read the <t>article</t> by Caleb Nelson ... in the November American Spectator." This is clearly a piece of writing in a publication (a magazine). The senses provided:

1. sense key article%1:10:00:: : nonfictional prose forming an independent part of a publication. This fits perfectly: a magazine article.
2. article%1:03:00:: : one of a class of artifacts, e.g., an article of clothing. Not relevant.
3. article%1:10:02:: : a separate section of a legal document. Not relevant.
4. article%1:10:01:: : (grammar) a determiner. Not relevant.

The best sense is 1. So output: {"sense_index": 1}


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: recent
Target surface form: recent
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.

Candidate senses:
1. sense_key=recent%5:00:00:new:00 | definition=new | examples=recent graduates; a recent addition to the house
2. sense_key=recent%5:00:00:past:00 | definition=of the immediate past or just previous to the present time | synonyms=late | examples=a late development; their late quarrel

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content: We are asked to perform word sense disambiguation for the word "recent" in the given context. The target lemma is "recent" and the surface form is "recent". The context includes: "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." So "recent" modifies "math major", meaning Caleb Nelson recently graduated as a math major. There are two candidate senses: sense 1 is defined as "new" with examples like "recent graduates; a recent addition to the house". Sense 2 is defined as "of the immediate past or just previous to the present time", synonyms "late", examples "a late development; their late quarrel". In context, "recent math major" means he was a math major not long ago, so it refers to something that happened in the immediate past. Sense 2 seems to fit perfectly: "of the immediate past or just previous to the present time". Sense 1 "new" could also apply, but sense 2 is more precise because it emphasizes pastness relative to the present. The example "recent graduates" is listed under sense 1, but actually "recent graduates" could also be interpreted as graduates who graduated recently, i.e., of the immediate past. However, the glosses distinguish them: sense 1 is simply "new" (perhaps in the sense of being new to a role or state), while sense 2 explicitly mentions "immediate past". The phrase "recent math major" likely means he completed his major recently, so he is a recent graduate in that major. The context emphasizes that he is a recent graduate, so sense 2 (past) is a better fit because it highlights the temporal recency. Sense 1 might be more about being new to the field, but in this context, it's about the timing of his graduation. Therefore, sense 2 is chosen.

provider: AtlasCloud


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: major
Target surface form: major
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.

Candidate senses:
1. sense_key=major%1:18:00:: | definition=a commissioned military officer in the United States Army or Air Force or Marines; below lieutenant colonel and above captain
2. sense_key=major%1:18:02:: | definition=British statesman who was prime minister from 1990 until 1997 (born in 1943) | synonyms=John Major, John R. Major, John Roy Major
3. sense_key=major%1:18:01:: | definition=a university student who is studying a particular field as the principal subject | examples=she is a linguistics major
4. sense_key=major%1:09:00:: | definition=the principal field of study of a student at a university | examples=her major is linguistics

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to disambiguate "major" in the context: "Caleb Nelson (himself a recent math major at Harvard)". The target word is "major", and the surface form is "major". The context shows it's referring to a person who is a "math major" at Harvard, meaning a student studying mathematics as their primary subject. So it's about a university student's field of study.

Let's examine the candidate senses:

1. military officer sense: not matching, context is academic.
2. British statesman: not matching, no mention of John Major.
3. a university student who is studying a particular field as the principal subject. Example: "she is a linguistics major". This fits perfectly: "math major" means a student whose principal subject is math.
4. the principal field of study. Example: "her major is linguistics". This would refer to the subject itself, not the person. For example, "Her major is linguistics" vs. "She is a linguistics major." In the context, it says "himself a recent math major", which is referring to the person, not the field. So sense 3 is the person, sense 4 is the field. The phrase "a recent math major" means he recently graduated as a math major (student), so it's the student sense.

Thus, the best indexed sense is 3.

Return JSON: {"sense_index": 3}


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: most
Target surface form: Most
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.

Candidate senses:
1. sense_key=most%4:02:00:: | definition=used to form the superlative | synonyms=to the highest degree | examples=the king cobra is the most dangerous snake
2. sense_key=most%4:02:01:: | definition=very | examples=a most welcome relief
3. sense_key=most%4:02:02:: | 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

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given the target lemma "most" and surface form "Most" in the context. The context is: "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." So "Most" is used as an adverb modifying the adjective "important"? Actually, "Most important of all" is a phrase where "most" is an adverb forming the superlative of "important" (most important). But note the phrase "Most important of all" is a set phrase meaning "the most important thing". Here "Most" is used as a superlative adverb.

We have three candidate senses:
1. sense 1: used to form the superlative, synonyms: to the highest degree, example: "the king cobra is the most dangerous snake"
2. sense 2: very, example: "a most welcome relief"
3. sense 3: (of actions or states) slightly short of or not quite accomplished; all but; synonyms: about, almost, nearly, etc. Example: "the job is (just) about done"

In the target sentence, "Most important of all" means "the most important" or "supremely important". It is forming the superlative of "important". It is not "very important" (sense 2) because "most important of all" is a clear superlative, and sense 2 is used without comparison, like "a most welcome relief" meaning "a very welcome relief". Here, "of all" indicates a comparison among all things, so it's the superlative use. Sense 3 is completely off because it's about "almost".

Thus, sense 1 is correct.

Answer: {"sense_index": 1}


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: important
Target surface form: important
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.

Candidate senses:
1. sense_key=important%3:00:00:: | definition=of great significance or value | synonyms=of import | examples=important people; the important questions of the day
2. sense_key=important%3:00:04:: | definition=important in effect or meaning | synonyms=significant | examples=a significant change in tax laws; a significant change in the Constitution
3. sense_key=important%3:00:02:: | definition=of extreme importance; vital to the resolution of a crisis | synonyms=crucial | examples=a crucial moment in his career; a crucial election
4. sense_key=important%5:00:00:influential:00 | definition=having authority or ascendancy or influence | synonyms=authoritative | examples=an important official; the captain's authoritative manner
5. sense_key=important%5:00:00:immodest:02 | 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

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given: Target lemma: important, target surface form: important, context: a paragraph where the phrase "Most <t>important</t> of all, schools should have principals with a large measure of authority ..." The context emphasizes that this is the most significant point. Let's examine the candidate senses:

1. sense_key=important%3:00:00:: | definition=of great significance or value | synonyms=of import | examples=important people; the important questions of the day
2. sense_key=important%3:00:04:: | definition=important in effect or meaning | synonyms=significant | examples=a significant change in tax laws; a significant change in the Constitution
3. sense_key=important%3:00:02:: | definition=of extreme importance; vital to the resolution of a crisis | synonyms=crucial | examples=a crucial moment in his career; a crucial election
4. sense_key=important%5:00:00:influential:00 | definition=having authority or ascendancy or influence | synonyms=authoritative | examples=an important official; the captain's authoritative manner
5. sense_key=important%5:00:00:immodest:02 | 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

In the context: "Most important of all" is a common phrase meaning the most significant point. It is used to emphasize the importance of what follows: schools should have principals with authority. This sense aligns with sense 1: "of great significance or value". Sense 2 is similar, but sense 1 is more general and direct: "of great significance or value". Actually, sense 2 says "important in effect or meaning" with example "significant change", but sense 1 is the primary sense. Sense 3 is "crucial", which might fit, but "most important of all" is a general expression of high significance, not necessarily related to a crisis. Sense 4 is about having authority, but here the word modifies the whole clause "schools should have principals...", it doesn't describe a person ("important official"). Sense 5 is about a pompous air, which is not applicable. So, the best sense is sense 1.

Thus, the answer is sense_index 1.

Return JSON: {"sense_index": 1}


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: school
Target surface form: schools
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.

Candidate senses:
1. sense_key=school%1:14:00:: | definition=an educational institution | examples=the school was founded in 1900
2. sense_key=school%1:06:00:: | definition=a building where young people receive education | synonyms=schoolhouse | examples=the school was built in 1932; he walked to school every morning
3. sense_key=school%1:09:00:: | definition=the process of being formally educated at a school | synonyms=schooling | examples=what will you do when you finish school?
4. sense_key=school%1:14:02:: | 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. sense_key=school%1:28:00:: | 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. sense_key=school%1:14:03:: | definition=an educational institution's faculty and students | examples=the school keeps parents informed; the whole school turned out for the game
7. sense_key=school%1:14:01:: | definition=a large group of fish | synonyms=shoal | examples=a school of small glittering fish swam by

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content: We need to disambiguate "schools" in the text. The text says: "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." It's about educational institutions, and specifically about a principal having authority over faculty, curriculum, and student discipline. That fits the first sense: "an educational institution" (sense 1). There's also sense 6: "an educational institution's faculty and students" - but here "schools" is the whole institution, and we are talking about the principal's authority over the faculty, curriculum, and discipline. So it's the institution as an entity. Sense 1 is "an educational institution", and the example: "the school was founded in 1900". The context is about the best schools being free of outside interference and governed by a powerful head. This is the institution. Sense 6 would be "the school keeps parents informed; the whole school turned out for the game" - but that's more about the people in the school. Here we're talking about the structure, governance, etc. So sense 1 is the best fit. Let's check: sense 1 is school%1:14:00::. Sense index is 1? Actually the list starts with 1, but we need to return the index number from the provided list. The list has 1 for the first, 2 for the second, etc. So sense 1 is index 1. But we need to choose the single best. Yes, sense 1 is the best. Let's return {"sense_index": 1}.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: principal
Target surface form: principals
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.

Candidate senses:
1. sense_key=principal%1:21:01:: | definition=the original amount of a debt on which interest is calculated
2. sense_key=principal%1:18:00:: | 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. sense_key=principal%1:18:01:: | definition=an actor who plays a principal role | synonyms=star, lead
4. sense_key=principal%1:21:02:: | definition=capital as contrasted with the income derived from it | synonyms=corpus, principal sum
5. sense_key=principal%1:18:03:: | definition=(criminal law) any person involved in a criminal offense, regardless of whether the person profits from such involvement
6. sense_key=principal%1:18:02:: | definition=the major party to a financial transaction at a stock exchange; buys and sells for his own account | synonyms=dealer

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content: We are given the target word "principals" in the context of schools. The sentence is: "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." The candidate senses include "the educator who has executive authority for a school" as sense 2. The context clearly refers to the head of a school, so sense 2 is the correct match.

provider: Together