Grammar, Rhetoric, and Style

Overview

This essay focuses on grammar, specifically on understanding that grammar is much more than just the rules that we have been taught. Rather, grammar can be used rhetorically—with an understanding of the writing situation and making appropriate choices regarding the structure of the sentences, the use of punctuation, using active or passive voice, etc. In other words, this essay focuses on using grammar to influence a piece of writing’s style, rather than focusing on the correctness of the grammar. Readers are encouraged to look at the writing that they see in their casual or research reading and evaluate the grammar of those pieces to gain a better understanding of how they can control their own use of grammar.


Grammmar.1 The mere word makes adults weep, children run and hide, and dogs howl. All right, perhaps I am exaggerating just a bit; not all of us hate grammar. There are even people who actually like grammar. However, the general aversion to the word “grammar” is such that the word is hardly ever used in polite company. And, if your composition professor is anything like me, she or he tries to avoid the word in your class.

Yet grammar should not be so disrespected. Believe it or not, most people like grammar until their junior high school English teacher gets ahold of them and presents grammar as a set of rules, a set of “Thou shalt not” commandments that you must abide by or be doomed to wander in the darkness of a poor grade. Max Morenberg, author of the book Doing Grammar, writes:

We are born to love language and everything associated with it— rhythm, rhyme, word meanings, grammar. If you want to make a three-year-old child roll on the floor laughing, just tell her a riddle, or alliterative words, or read her Dr. Seuss’s lilting rhythms and rhymes about cats in hats or elephants who are ‘faithful, one hundred percent’ or Sam I Am eating green eggs and ham on a boat with a goat. Listen to a child in a crib entertaining himself by repeating sounds and syllables, playing with language. Think about the games you played in kindergarten by creating strange words like Mary Poppins’ supercalifragilisticexpialodotious. Keep a ten-year old entertained on a car trip by producing odd sentences in a ‘Mad Libs’ game. Then ask an eighth grader what subject she hates most. The answer invariably will be grammar. We’re born to love grammar. We’re taught to hate it. (vii-viii)

When young and learning how to use language, we learn grammar through trial and error. When my daughters were around two years old, they (constantly) wanted me to pick them up. They would come up to me, hold up their arms, and I would ask them, “Do you want me to hold you?” Eventually, they would come up to me, hold up their arms, and say, “hold you.” They learned the construction “hold you” to mean “hold me.” I would correct them and explain to them “if you want me to pick you up, you say ‘hold me.’” Before too long they caught on and started saying “hold me” when they wanted me to pick them up. They learned by mirroring my speech and by receiving feedback on their grammar. As we grow older, we still learn through trial and error, but we also learn the rules. Now, instead of a parent’s gentle correction, we are informed of our errors through the fiery correction of a teacher’s red pen.

Grammar, the way that it is typically taught, is a collection of rules that we are supposed to follow, and it is these rules that most of us have issues with. After all, we know how to speak; we form words and sentences intuitively, and people understand our meaning. So, who are these rule-mongering grammarians that think that they can tell us that we are doing it wrong? Or who force us, as my middle school English teacher did, to endlessly diagram sentence after sentence? Why do they take something that we love as children and warp it to the point that we can’t stand it?

Grammar doesn’t have to be this way. It shouldn’t be this way. We shouldn’t need someone to tell us that we are wrong, and then to make us memorize a bunch of rules in order to speak or write. What grammar should be is a tool to help us better communicate with our audience—a tool that we are controlling, rather than one that controls us. Grammar should be a tool that we use to fit our language to our purpose and our audience.

Grammar and Its Rhetorical Use

The rules are there for a reason. Grammar rules are concerned with correctness—to make sure that we are following the accepted guidelines of the language. However, grammar isn’t all about rules. Instead, grammar is about making meaning. People understand us because we are using gram- mar—we are arranging our words in a certain order, and because of that, our audience understands us. For example, if I said, “store went to Jim the,” you’d probably ask, “What?” But if I used the same words and arranged the words according to the grammar that I absorbed at a young age, I would say, “Jim went to the store.” By arranging the words according to what those listening to me expect from my grammar, my audience would know exactly what I meant. And this awareness of what the audience needs is the heart of what I am talking about—that grammar has a rhetorical use.

Grammar simply means “a system that puts words together into meaningful units” (Morenberg 4). We’ve already seen how that works in the earlier example of “Jim went to the store.” As we create lengthier and more complex sentences, we incorporate punctuation such as commas and semi-colons, consider pronoun/antecedent connections, carefully think about verb shifts and a host of other issues that can affect the meaning of our words. This is what most people think of when they hear the word grammar. However, this doesn’t have to be that big of a concern, as grammar is best learned by using the language, rather than through systematic study of the rules. In fact, I have had many older, so-called non-traditional students in my composition classes throughout the years, and they are generally more adept at grammar usage than my “traditional” eighteen to twenty-year-old students. This is not because they have studied the rules of grammar more thoroughly; most of my older students confess that they haven’t thought about grammar for many years. This is simply because they have used the language, and have experience using it in many different contexts, for a greater length of time.

Rhetoric is a word that most of us have heard, but we may not really understand what it means. It is a word that is often thrown around negatively, and often in political discussions, such as, “Well, the president may think that way, but I’m not falling for his rhetoric.” But the term really shouldn’t have such a negative connotation. Simply defined, rhetoric is “a way of using language for a specific purpose.” The rhetorical situation of a piece of writing is everything surrounding it—who the audience is, the purpose for writing it, the genre of the writing, etc. Knowing this helps us know how to use language to accomplish the purpose of the writing, and grammar is part of that use of language. English professor Laura R. Micciche expands on the rhetorical role of grammar:

The grammatical choices we make—including pronoun use, active or passive verb construction, and sentence construction—rep- resent relations between writers and the world they live in. Word choice and sentence structure are an expression of the way we attend to the words of others, the way we position ourselves in relation to others. (719)

When we write, we can carefully choose the grammar that we use to make our writing effective at conveying our meaning, but also give the audience a sense of our own personality. This brings us to a third word that needs to be defined: Style.

Grammar and Style

Style is perhaps the most visual aspect of rhetoric—we see authors’ style in their writing. Style refers to the choices that an author makes—choices about punctuation, word usage, and grammar—and those choices are influenced by the rhetorical situation that the author finds herself in. For example, consider the following sentences:

  • Katelyn was concerned that Chloe worked late every night.
  • It concerned Katelyn that every night Chloe worked late.
  • Chloe worked late every night, and Katelyn was concerned.
  • Every night Chloe worked late, and that concerned Katelyn.

Each of these sentences say the same thing, and the grammar is “correct” in each, but the sentence an author chooses depends on the style she wishes to use. The first sentence is the most straightforward, but the last two put the emphasis on Chloe rather than on Katelyn, which might be what the author wants to do. Sometimes the style within a specific rhetorical situation is prescribed for us; for example, we might be told that we cannot use “I” in a paper. Sometimes the style is expected, but we aren’t necessarily told the rhetorical situation’s rules; we might be expected to use the active voice rather than the passive voice in our papers. And sometimes the situation is wide open, allowing us to make the grammatical style choices we like.

Also wrapped up in this issue of style is the concept of standard and preferred usage. Usage is simply the way we expect words to be used—and this doesn’t always follow the rules. For example, a famous line from the original Star Trek series tells us that the Enterprise’s mission is “to boldly go where no man has gone before.” This seems right—but there is a split infinitive in the phrase (no need to worry about what a split infinitive is right now). To abide by the rule, the line should say, “to go boldly where no man has gone before.” But that doesn’t sound as right to most of us, so a decision was made to break the rule and write the line according to the common usage of adding an adverb before the verb.

What usage is preferred is also dependent on the rhetorical situation of the text. As an example of the differences between standard and preferred usage, consider contractions. Most of the time when we speak, and often in informal writing, it is perfectly fine to use contractions like “can’t,” “isn’t,” or “aren’t;” contractions are standard usage. You may have been told in your composition class that using contractions is okay in your papers, but using contractions is not preferred in many rhetorical situations, as in a formally written research paper. We use the words “I” and “you” all the time when we speak, but we will find many writing situations where they aren’t acceptable (i.e. preferred). Knowing what usage is preferred takes a little insight into the rhetorical situation—you can read examples of the type of writing that you are asked to do, you can question friends who have already taken the course, you can seek advice from books or the internet, or you can ask your instructor. Since grammar, style, and usage are so closely related, and quite possibly they have already been introduced to you as the same thing, throughout this essay I will often refer to these types of style choices as grammar choices.

All Together Now

When we write, we are entering into a conversation with our reader, and the grammatical choices that we consciously make can show our readers that we understand what they want from us, and that we are giving them what they expect. In your academic writing, the rhetorical situation demands that you make grammar choices that are appropriate for college-level writers. Unfortunately, these grammar choices are not static; they will change—perhaps only slightly, perhaps greatly—as your writing situation changes, as you write for different teachers, courses, or disciplines. In your other writing, the rhetorical situation may call for an entirely different set of grammar choices.

Here’s an example of how the rhetorical situation affects grammar usage. You need to express an idea concerning the need to recycle. In the first rhetorical situation, you are speaking to your friends, people that you have known since you were five years old. In such a situation, it might be acceptable for you to say, “It ain’t rocket science, bonehead. Recycle that junk and save the Earth.” If you’re speaking to your mother, you might say, “Mom, that can go in the recycling bin instead. Let’s save the planet.” If you are writing about this for an academic audience, you might instead say, “We must always consider the consequences of our actions. Throwing recyclable materials in the trash results in overflowing landfills, land and water pollution, and an increased strain on raw materials. However, recycling glass, metal, and paper reduces our consumption of these materials as well as lowers the fossil fuel energy needed to create new products.” The example should not suggest that longer sentences are more correct, although the academic audience example is considerably longer than the other two. Hopefully, if I have done it right, the academic audience example is longer simply because I am proving my point, not because I’m trying to sound smart by using more words. But the grammar has also changed. In the first example, I used “ain’t,” which is not considered grammatically correct for most academic audiences, but the use of which is quite common in many varieties of spoken English. In the second example I used the con- traction “can’t,” which, again, in many academic writing situations would be frowned upon. In the final example, I have attempted to use “standard” grammar, the grammar that the academic rules say I should use, as I know that that particular audience would expect me to do so.

In many academic writing situations, the work is assessed, in part, on how well the writer adheres to the rules. If I used the style and grammar of the first example in a paper for my Environmental Science class, you can imagine what could happen. Writing an academic paper as if I was talking to my friends would probably negatively affect my grade. However, the poor grade wouldn’t mean, “your grammar is wrong,” even if my instructor phrased it that way. Instead, what the grade would mean is that I did not use the appropriate grammar required for the rhetorical situation.

Using Grammar Rhetorically for Style

Grammarian and textbook author Martha Kolln asks us to look at sentences as a series of slots into which we place words (5). We know what to put into certain slots; for example, in the “subject” slot we know we need a noun or a pronoun, and in the “verb” slot we need, well, a verb. Knowing just these two slots, I can make a good sentence: “I laughed.” As sentences get more and more sophisticated, more slots become available. For example, adding an adverb slot, I can create the following sentence: “I laughed loudly.” This is a basic element of the rules—the rules tell us what we are allowed to put into the slots.

So then, how do we move past the rules? How does a writer use grammar rhetorically? First and foremost, you use grammar this way by being conscious of the choices that you are making. Remember, when you write, you aren’t simply putting words on paper; you are constructing a conversation with a reader. You make conscious choices about your topic, your title, and your word choice, as well as many other choices, in order to carry on that conversation—grammar is just part of the many choices that you can use to your advantage when you are using language for your specific purpose. It might help you to see how this is done by looking at works that have been written for a variety of audiences and trying to figure out why the authors made the grammatical choices that they did.

Throughout the rest of this essay, I will present several examples of writing, and I will look at what each author has chosen to put into their sentence slots and why they made those choices. The first example is a paragraph from the manual for the video game Fallout 3:

Nuclear war. The very words conjure images of mushroom clouds, gas masks, and bewildered children ducking and covering under their school desks. But it’s the aftermath of such a conflict that truly captures our imagination, in large part because there’s no real-world equivalent we can relate to. Mankind may have witnessed the horror of the atomic bomb, but thankfully we’ve somehow succeeded in not blowing up the entire planet. At least, not yet. (Vault Dweller’s Survival Guide 3)

This paragraph violates many of the rules that I learned as a developing writer. For example, I see the contractions it’s, there’s, and we’ve, and a conjunction, but, starts a sentence. I see the preposition to ending a sentence—a definite no-no, if I remember my grammar rules. Also, as I write this on my computer, my word processor is very kindly informing me that there are two fragments in this paragraph. I believe that Ms. Herrema, my eighth grade English teacher, would cringe if she read this paragraph in a student paper. Yet I think it unlikely that you noticed all of these “errors” in the paragraph as you read it. Why didn’t you? Is it because you are ignorant of the rules of grammar? Absolutely not! Assuming that you didn’t notice them, you didn’t notice them because taken all together, the paragraph flowed well. The fragment sentence, Nuclear war, didn’t bother you—in fact, it probably grabbed your attention. The contractions didn’t bother you because it sounded like someone was speaking to you. And they were. The intended audience of the writer is those who would buy and play video games. (That might include you—it does include me.) As such, the author knowledgeably chose the language, the grammar, of the game manual in order to maintain the interest of the audience. We speak with con- tractions; the author uses contractions. We speak in fragments; the author uses them. Notice that the author is using the fragments ominously. He (or she, but probably they—much professional writing is team written) begins with Nuclear war. Culturally, we have, for the past seventy years or so, lived with the knowledge that a nuclear war could happen. Those two words conjure up such dark and depressing images that all the author needs to do is say them, and we’re hooked. Likewise, the last sentence of the paragraph is also a fragment, ominous, and attention grabbing: At least, not yet. We have dodged this atomic bullet until now, but it could still happen—and that is what the author wishes to leave us with.

Let’s look at how the commas are used in this paragraph. The first commas that we see are in the list: mushroom clouds, gas masks, and bewildered children. Why does the author put those commas there? Is it because the rules tell him to? Yes—and no. Sure, the rules tell us to put those commas in there, but if we’re relying on the rhetorical use of grammar, we’ll also use them in exactly the same way. A comma indicates a pause in a sentence, a pause that the audience needs in order to get the meaning the author intends to give them. Read that sentence out loud without the commas: The very words conjure images of mushroom clouds gas masks and bewildered children ducking and covering under their school desks. Without the commas, it sounds weird. Your audience might even see this as five- item list of mushroom, clouds, gas, masks, and bewildered children, rather than the three-item list that it is. If the author’s meaning is for the audience to see mushroom clouds and gas masks and bewildered children, regard- less of the rules, he would add a comma to make them pause, just a bit, at certain points.

Let’s move from the popular to the academic in this next example:

The typewriter is effectively a lost technology, occupying a strange, interstitial space in the broader field of media history, a fulcrum between the movable type of modern print culture and the malleable digital information of postmodern electronic culture. I argue that consideration of the typewriter as a writing system thus provides critical purchase on this field precisely to the extent that the machine itself is ephemeral and ultimately obsolete. (Benzon 93)

Did you get all that? You probably noticed the difference in vocabulary between this paragraph and the passage from game manual. This author is definitely writing for a different audience; in this case, he is writing for English scholars and educators. If we look at the first sentence as a series of slots, we see typewriter in the subject slot, is in the verb slot, and technology in the object slot. But we also see effectively and lost in the sentence, occupying two optional slots. Lost is positioned in an adjective slot and describes technology. What kind of technology? Lost technology. Effectively is positioned in an adverb slot, and as such it modifies the verb. Is what? Is effectively. We could have eliminated these two modifiers and the sentence would have made sense. But Benzon, the author, did not want to say that “The typewriter is a technology.” He wanted to say that it was effectively a lost technology. Typewriters still exist, and people still use them, although they are effectively a lost technology.

Notice, too, that there are other optional slots that were not filled. Typewriter, as a noun, has an optional adjective slot, too. But instead of describing the typewriters, Benzon chooses not to fill in that slot. Doing so might restrict the noun—adding an adjective to describe what type of typewriters are lost technology could limit the meaning. Adding an adjective like red, old, or dusty would say that typewriters that are blue, new, or clean are not lost technology.

Benzon also chooses to use the grammatical device of parallelism in the phrase, “a fulcrum between the movable type of modern print culture and the malleable digital information of postmodern electronic culture.” Movable type runs parallel to malleable digital information. In both situations, we see nouns (type and information) preceded by filled adjective slots. Movable and malleable even sound similar. Benzon opted to fill in another adjective slot before information and told us that it was digital information but decided not to do so before type. This is acceptable, of course, because type does not need any additional description, but we certainly need to know what sort of information is malleable.

Finally, we see in this example that Benzon uses I. This convention is generally acceptable in the discipline of the humanities, and knowing that his audience would accept this, Benzon has decided to use I. He also uses the active voice, writing, “I argue that consideration of the typewriter as a writing system…” The author, I, is doing something, arguing. (In this case, my middle school English teacher’s advice to write in the active voice has been justified.) Had I not told you that both the use of I and the active voice were acceptable in the humanities, analyzing the previous paragraph would have shown that this was true.

And now let’s try one more, this time from an academic article from the sciences:

Animals were randomly assigned to three treatment groups with five pigs per group in a completely randomized design. All pigs were fed the basal diet during the initial 7 day period. Pigs were then fed treatment diets during the next three 7 day periods and all pigs received the basal diet during the final two 7 day periods. (Stewart et al. 169)

This excerpt comes from an article in the American Journal of Animal and Veterinary Sciences, so who do you think is the intended audience? If you said, “circus clowns,” you might want to try again.

Obviously, we see vocabulary that is intended for veterinarians or students of veterinary medicine. The main reason that I have offered this pas- sage to you, aside from the fact that I enjoy torturing people with language, is that we can see two differences between this piece of academic writing and the previous piece. The first is that there is no use of I. Why didn’t the authors say, “We fed the pigs the basal diet during the initial 7 day period?” The reason is that, unlike in the humanities disciplines, the use of the personal pronoun is not expected by a science audience. Using it would be counter to the expectations of the audience, so it isn’t used. (Score one for the middle school English teacher who told me not to use I.)

The second difference from the Benzon passage is that the subjects of the sentences aren’t doing anything; this passage is written in the passive voice. Whereas Benzon could say, “I argue,” which showed the active subject I doing something (arguing), in this piece, the pigs are passive receptors of the food. They sit there; food is given to them. If this was recast in active voice, we might end up with, “All pigs ate the basal diet during the initial 7 day period.” Unlike the humanities disciplines, the sciences have a tendency to prefer the passive voice. Again, if I hadn’t just told you these two conventions of science writing, had you rhetorically analyzed the piece, analyzed its audience, purpose, and grammar, you would have seen that these conventions exist.

If you’d like a fourth example, consider this essay that you are reading. Ask yourself why I made the grammatical choices that I did. I use “you,” I use contractions, I tend to use the active voice. There a few fragment sentences in here—the first sentence of the essay is a fragment. Why would I write with these rule violations?

Did you notice the “errors” I listed above as you read through the paper? I am guessing that you did not, or at least you did not catch all of them. If I have done my job right, I have successfully entered into a conversation with you—a first year writing student—and spoken to you using a grammar that is comfortable and appropriate for you. How did I do?

With these four examples, I’ve only given you a taste of how looking at grammar choices rhetorically can help you understand an author’s intended audience, that audience’s expectations, and how the author, by choosing his or her grammar to reflect those needs, attempted to enter into a relationship with the audience. You could spend quite a bit of time on any of those examples and pull even more insights from the grammar that the authors use, but given the scope of this essay, I believe that I can now safely let you go, believing that you now have a solid understanding of how writers—and that includes you—make careful choices with their grammar and use it as a tool to more effectively communicate with their intended audience.

Note

1. Throughout this essay, I will use some simple grammar terms such as noun, pronoun, adjective, adverb, and so on. I am, perhaps wrongly, assuming that you will understand these terms. If I have erred in my assumption, please accept my apologies. There are many ways to discover the meanings of these terms, the first of which is your instructor. Other resources include handbooks, internet sources, and your friends.

Works Cited

Benzon, Paul. “Lost in Transcription: Postwar Typewriting Culture, Andy Warhol’s Bad Book, and the Standardization of Error.” PMLA, vol. 125, no. 1, 2010, pp. 92–106. JSTOR, www.jstor.org/stable/25614438.

Kolln, Martha. Rhetorical Grammar. Longman, 2003.

Micciche, Laura R. “Making a Case for Rhetorical Grammar.” College Composition and Communication, vol. 55, no. 4, Jun.2004, pp. 716-737. ProQuest, http:// search.proquest.com.ezproxy.gvsu.edu/docview/62073590?accountid=39473.

Morenberg, Max. Doing Grammar. Oxford UP, 1997.

Stewart, L. L., Beob G. Kim, B. R. Gramm, R. D. Nimmo, and H. H. Stein. “Effects of Dietary Carbadox on Apparent Ileal Digestibility of Amino Acids in Weanling Pigs.” American Journal of Animal and Veterinary Sciences, vol. 5 no. 3, 2010, pp. 168-174. https://nutrition.ansci.illinois.edu/sites/default/files/ AmJAnimVetSci5.168-174.pdf

Vault Dweller’s Survival Guide. Bethesda Softworks. 2008.


 

Teacher Resources for Grammar, Rhetoric, and Style by Craig Hulst

Overview and Teaching Strategies

When I ask my students about the weaknesses of their own writing, the vast majority state that grammar is an issue for them. Usually what they mean is that they do not remember the rules that they were taught and believe that without the rules, their writing must be weak. This essay is designed to be used to help students understand that grammar is more than just rules. Grammar can be used as a tool to influence the style of the piece, and students already implicitly have some understanding of how to use it that way.

This essay would best be used when a teacher is talking about either grammar or style. When talking about grammar, it could be linked with a discussion of why first year writing courses do not typically spend much time on the rules of grammar. When discussing style, it can be used in conjunction with understanding how the rhetorical situation influences style, and how grammar is one element of choosing an appropriate voice and style for that particular situation. It might be particularly useful when discussing revising, rather than drafting.

Questions

  1. Before reading this piece, what was your reaction to hearing the word grammar? Did you like studying grammar? Did you hate it? After reading this piece, has your impression of the word changed at all?

  2. Has grammar only been presented to you as a set of rules before? Why do you think it was taught that way?

  3. In the personal example in the essay, the author wrote about his daughters learning to say “hold me” instead of “hold you” at two years old, but grammar is constantly developing as we are constantly developing our language. Do you remember any of the moments when you realized that the way that you used the language needed to be adjusted, or when you discovered that your grammar usage was not correct? What was it?

  4. For the most part, it is less important that you understand all of the rules or grammatical terms than it is that you can recognize when something doesn’t sound right. However, this “sounds right” part of grammar can trip you up if you are trying to complete grammar exercises, as that usually means that you are responding to usage (the way most people seem to be using the grammar) instead of correctness (following the rules). Usage and correctness are often the same, but many times they are not. Are there any times that you can remember where you were corrected for using grammar according to usage instead of correctness? Why do you think that the usage is different from the rule? (Note to teacher: this question might best be used in conjunction with a grammar exercise to illustrate the difference of usage and correctness, possibly followed with a discussion of the style benefits of either).

  5. Choose a passage from an essay that you have written. What grammatical choices did you make? What choices (word choice, the choice to fill in a slot or not, parallel structure, etc.) did you make? Which choices did you choose not to make? Should/can you continue to make choices that will give your audience what they expect to see?

Activities

Rhetorical Grammar Analysis

There are essays in Writing Spaces that talk about reading rhetorically (See Mike Bunn’s and/or Karen Rosenberg’s essays, for example). Combining this essay with one of those, ask students to look specifically at the grammar of a chosen piece of writing. Starting simply, ask them to look at the use of pronouns or contractions. What does the way that those parts of speech are used (or not used) say about the author’s choices, about the intended audience? Move on to modifiers and look at the use of adjectives and adverbs. Are they widely used or are they sparse? Are there two or three modifiers for a noun or one? What do those decisions say about the rhetorical situation? Choose any other element of grammar and continue the analysis.

 

Revising Grammar for Style

Have students take a paper that they are revising and have them specifically look at their grammar. Ask them to identify their audience and the expectations of their writing. If they have already tried their hands at the Rhetorical Grammar Analysis activity, they might be able to apply what they have learned about how the author used grammar to create an appropriate style to their own writing. Otherwise, ask them about the level of formality that is expected in their writing and whether or not their use of grammar (pronoun usage, including gender-specific pronouns; contractions; complexity of sentence construction; etc.) supports that. Students might choose specific sentences and rewrite them (making active voice passive, adding modifiers, changing the verb tense, etc.) to see how the style of the sentence can be altered by grammatical choices.


This essay was written by Craig Hulst and published as a chapter in Writing Spaces: Readings on Writing, Volume 3, a peer-reviewed open textbook series for the writing classroom. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0), and it appears here with minor changes. Please keep this information on the material if you use, adapt, and/or share it. 

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