Meaning: 'Enjoyed' means to have taken pleasure in or benefited from something, indicating that ancient Greece had a significant and positive experience in advancing mathematics.

Wrong options:

• marked: 'Marked' implies a distinction or indication, which does not convey the sense of positive experience or achievement in this context.
• reviewed: 'Reviewed' suggests an evaluation rather than an active engagement or progress, making it unsuitable for describing the historical context of mathematical advancement.
• expected: 'Expected' indicates anticipation rather than actual achievement, which does not accurately reflect the historical reality of ancient Greece's contributions to mathematics.

Correct answer: failing

Explanation: The word 'failing' appropriately indicates a lack of success in teaching mathematics at school, which contrasts with the previous statement about progress. This juxtaposition enhances the overall meaning of the sentence.

Meaning: 'Failing' means not succeeding in achieving something, in this case, the teaching of mathematics in schools, highlighting a significant gap despite the progress made.

Wrong options:

• waiting: 'Waiting' implies a pause or delay, which does not convey the active failure to teach mathematics, making it contextually inappropriate.
• hesitating: 'Hesitating' suggests uncertainty or indecision, which does not accurately reflect the failure to teach, as it implies a lack of action rather than an unsuccessful attempt.
• hoping: 'Hoping' indicates a desire for something to happen, which does not fit the context of actively failing to teach mathematics.

Correct answer: radical

Explanation: The word 'radical' fits well as it describes a significant or fundamental change in perspective regarding how mathematics should be learned. It aligns with the context of the punchline, emphasizing a transformative idea.

Meaning: 'Radical' means relating to or affecting the fundamental nature of something, indicating a profound shift in understanding about learning mathematics after school.

Wrong options:

• rational: 'Rational' refers to being based on reason or logic, which does not convey the transformative aspect implied in the context of the punchline.
• radish: 'Radish' is a noun referring to a type of vegetable, which is completely unrelated to the context of mathematics and does not fit grammatically or contextually.
• radius: 'Radius' is a geometric term that does not relate to the idea of a significant change in learning mathematics, making it contextually irrelevant.

Correct answer: leave

Explanation: The word 'leave' fits grammatically and contextually as it indicates the action of exiting school, which is necessary for the punchline to make sense. It suggests that learning mathematics could improve after formal education ends.

Meaning: 'Leave' means to go away from a place, in this case, school, indicating that the opportunity for better learning arises after this departure.

Wrong options:

• enter: 'Enter' implies beginning a phase rather than exiting it, which contradicts the idea that learning improves after leaving school.
• graduate: 'Graduate' suggests completing school, but it does not convey the same sense of departure as 'leave,' which is more aligned with the context of the punchline.
• go: 'Go' is too vague and does not specifically indicate the action of leaving school, making it less precise in this context.