This poem by Billy Collins is about teaching poetry. To address your question, I will break down my analysis according to the six elements you listed.
Situation: The speaker has the perspective of a teacher. The “them” in the poem is presumed to be the speaker’s students. There are neither discernible characters nor settings.
Purpose: The speaker discusses the various ways he wants his students to approach the study of poetry. The last two stanzas address how the students instead beat a poem “with a hose” in order to “torture a confession out of it.” The contrast between these two parts of the poem underscores the message: poetry does not provide straightforward answers, which frustrates many who study it.
Imagery: Some notable images from the poem include “holding it up to the light like a color slide,” “feel the walls for a light switch,” and “waterski across the surface of a poem.” These images are memorable because they illustrate the various ways someone can approach a poem. Poems can be beautiful, mysterious, and even fun.
Diction: The connotation of the words in the first five stanzas is mostly positive. Words like “light” and “waving” are some examples. The diction, and thus tone, shifts in the last two stanzas. Words like “rope,” “torture,” and “beating” are violent and echo the negative reaction that students have to a poem.
Economy: The poem is arranged into seven stanzas. While some stanzas are comprised of three lines, others contain two. The second stanza consists of only one line. The irregular arrangement of the stanzas mirrors the disorienting effect that poems have on the speaker’s students.
Rhythm: Like it’s organization, the poem’s rhythm is irregular. Despite this, a couple lines have an iambic construction. Line 4 (“or press an ear against its hive”) is written in iambic octameter. This pattern coincides with the subject matter of the line that uses a hive as a metaphor for poetic rhythm. The poem is also written in free verse, meaning it lacks a rhyme scheme. The lack of a regular rhyme scheme fits with the tone and purpose of the poem.