September 7, 2009
The KISS Grammar Printable Books Page
Raphael's
School of Athens
Detail of Plato & Aristotle, 1511, Fresco
Stanza della Signatura, 
Vatican Palace, Rome 
The Importance
of Method

     Although the essays in the preceding section address what KISS Grammar can do, perhaps the most important thing that KISS can do for students is to teach them the importance of method. Although many educators make fun of the Grandgrind approach to education (memorize and regurgitate), they continue to use it. In K-12, math may be the only subject in which teachers insist on “showing one’s work,” but the very fact that math stands alone may explain why our students have so much trouble with math. The importance of method in all areas of education is so important that I ask you to bear with me and briefly explore the educational research of Arthur Whimbey and Carol Dweck.
     In 1993, Arthur Whimbey et al. published Blueprint for Educational Change. One of the most important parts in that book is Whimbey’s report on his research. He attempted to distinguish the differences between what he called “strong students” (those who get A’s and B’s) and “weak students” (those who get D’s and F’s). He found two major differences. First, “strong” students break almost every task down into steps—methodical procedures. “Weak” students consider any task a one-shot job—either one knows how to do it, or one doesn’t. Second, “strong” students are very concerned with details. They will do whatever they need to in order to understand details and to use details in their work. “Weak” students don’t care about the details. 
     For years I used to devote an entire class period (a huge investment of time for me) to a presentation on Whimbey’s work. He gives, for example, a page of typical national exam questions and then discusses what strong and weak students said about how they “solved” them. We did several of them in class. One was “Which letter is as far away from K in the alphabet as J is from G?” (p. 7) Whimbey notes that several “strong” thinkers “admitted they counted with their hands in their pockets to avoid embarrassment—to conceal this hidden activity. The reason for their secrecy is that there is a common myth that counting on one’s fingers is a childish activity, reflecting lower mental ability when done by an adult.” Whimbey, however, argues that such efforts to handle details are not at all childish. They are characteristic of “strong thinkers.”
     But Whimbey explains still another important aspect of this example. The test is multiple-choice, and there are two possible answers to the question—“H” and “N.” Some people did the problem, arrived at “H,” but were frustrated, and apparently quit,” because “H” is not one of the possible answers. Good thinkers, however, are not discouraged by failure. They tried counting in the other direction and arrived at “N,” the correct choice on the exam. The class period devoted to this presentation helped (I hope) at least a few students, but I continue to be frustrated by the failure of many of my students either to break their writing down into some version of the “writing process” or to be concerned with details. I’ll skip the numerous possible examples related to writing, and focus on one related to KISS Grammar.
     Recently a student came to see me to discuss the course work. Among other things, she said she could not understand complements. I asked her for the rule on identifying complements. (“Ask ‘whom or what?’ after the verb.”) She had not memorized it. Apparently, this detail was not important. I pulled up the instructional material, went over the rule (which had “Memorize” written next to it), and turned to an exercise. “This word is a verb. What is its complement?” She hesitated, so I said “What answers the question “what?” after it. She told me. “So,” I said, “that word is the complement.” Then I asked her for the rule on how to identify the types of complements. (“If the complement describes the subject, it is a predicate adjective. If not, then if the complement equals the subject in any way, and if the verb in any way means equals, the complement is a predicate noun. If that is not the case, in our course, I will take indirect as direct objects. In other words, the only choice left is “direct object.” (This is discussed in more detail below.) Once again I had to lead her through the sequence, even though we had done this several times already in class. We repeated the process two or three times. Then she said, “Oh, I guess I can understand complements.” Many students are like her. They need to be led and re-led through the use of simple procedures several times before they “get it.”
     Carol Dweck, in Mindset (Ballantine, 2006), argues that the problem is deeply psychological. Her discussion of “fixed” and “growth” mindsets parallels Whimbey’s in many ways. Basically she argues that people with “fixed” mindsets believe that one either knows the answer or does not. Like Whimbey’s “weak” thinkers, they avoid both process (method) and details. People with “growth” mindsets, on the other hand, like Whimbey’s “strong thinkers,” thrive on challenges, on the possibility of failure, and they go out and find the methods they might need to succeed at a problem. But according to Dweck, it is not enough to simply inform students about the differences between “strong” (“growth”) thinkers and “weak” (“fixed-mindset”) thinkers. One has to repeatedly show people with fixed mindsets the importance of method. They need to learn that there are no stupid people—everyone can learn—if they learn how to learn. The KISS Approach to grammar is an excellent tool for doing this.
     The key to KISS is the ANALYTICAL PROCEDURES—the methods. Instead of giving definitions and a few simplistic examples, KISS gives students procedures (methods) that will enable them to identify all the major grammatical constructions. If KISS is spread over several years, as it should be, students will, in other words, be reinforced in the idea of both “method” and “details” at several different stages of their work.

KISS Level One - The Basics

Identifying Verbs 

     Perhaps the most difficult thing for students to do in their study of grammar is to learn how to identify verbs. Most textbooks define verbs as words that “show action or a state of being.” When I was sixty, I finally guessed that “state of being” may have originated because many of those verbs are forms (states?) of the verb “to be” -- “am,” “is,” “are,” “was,” and “were.” That makes sense, however, only after one can identify verbs. For students, it is pure nonsense -- non sense, as one philosopher loved to point out. 
     Approximately 80% of my college Freshmen cannot identify “was” or “were” as verbs. We have 28 “lessons” in which to enable them to identify clauses. Because they have a lot of other things to learn, in the first grammar lesson they are told to memorize “am,” “is,” “are,” “was,” and “were” as verbs, verbs that must always be underlined twice. If you have more time, you can add more words to this list, but the list is effective for making another point. There are some things that I expect students to always get right. The underlining of these five verbs is one of them. On the other hand, there are many mistakes that I expect students to make. As we go along, I explain these, but the point is important. Students are expected to make mistakes as they analyze sentences in the KISS Approach, but they should quickly learn that there are some things that they must always get right. Details are important.
     Beyond the listed verbs, students learn to identify verbs by practice. Definitions do not help. Thus, expect students to make mistakes. Brief in-class reviews of exercises are excellent for this purpose.

“Complements”

     Sometimes, more is less. Traditional grammars rarely discuss “complements.” Instead, they try to teach intransitive verbs, transitive verbs, linking verbs, and to define predicate nouns, predicate adjectives, indirect objects, and direct objects. Such instruction is not effective. Intransitive verbs are verbs that do not have a direct or indirect object. Transitive verbs have an indirect and/or a direct object. “Linking verbs” have a predicate adjective or a predicate noun. One problem here is that the textbooks give a sample list, always incomplete, of “linking verbs.” Thus students are forced to memorize an incomplete list, but may still be left wondering what type of verb “equals” is in “Two plus two equals four.” Another problem arises with “direct objects.” They are often defined as the words that “receive the action of the verb.” But what “action” does “books” receive in “They have five books”? (Every grammarian that I am aware of considers “books” in that sentence to be a direct object.)
     All of this ineffective and sometimes nonsensical “instruction” can be avoided by adding the concept of “complement.” A complement is any word that answers the question “whom or what?” after a verb. The question must be “whom or what?”, not “when?” “where?” “why?” “how?” or anything else. Teaching students to identify complements is easy, but, as noted above, many students will resist mastering a method (how) rather than facts (what). But as I tell my students, many instructors in other fields (electronics, automotive, math, etc.) have complained that students answer every question as if it were a “what” question. Instructors ask “How?” Students tell them “what.” Instructors ask “Why?” Students tell them “what.” Thus, the very act of focusing on the distinction between “whom or what” and all the other possible questions may, in itself, improve students’ grades -- they will stop, think, and answer the question that is being asked.
     There are five, and only five types of complements -- zero (none), predicate adjectives, predicate nouns, indirect objects, and direct objects. Having found a complement to a verb, students can learn to identify its type by using a series of questions.

1. Does the complement describe the subject? If so, it is a predicate adjective. If not
2. Does the complement in any way equal the subject and does the verb in any way mean “equals”? If so, the complement is a predicate noun. If not
3. Does the complement indicate what the verb is done to or for? If so, it is an indirect object. If not
4. The complement has to be a direct object.
The preceding sequence does not give traditional definitions (thereby excluding both the distinctions in the three kinds of verbs and the nonsensical definition of “direct object”), but it always works. 
     It also provides students with a systematic, easily applied procedure for identify the S/V/C patterns in any text: 
1. Find a verb. 
2. Find its subject by asking “Who or what?” before the verb. 
3. Find its complement by asking” Whom or what?” after the verb. 
4. Use the sequence for determining the type of the complement (zero, predicate adjective, predicate noun, indirect and/or direct object). 
5 Check to see if there is another verb in the sentence.
It’s important to teach students to work systematically. Some students will underline a verb here (without finding its subject), a complement there, etc. They never know when they are done, and they usually do a poor job. Learning to work systematically is important in all subjects (including math), and KISS Grammar can help students to learn that.
     “Complement” is an important concept for another reason. The complement of one verb can never be the subject of another verb. In a sentence such as “They saw the man who wrote the book,” many students have trouble identifying the subject of “wrote.” If, however, they learn this rule, they are forced into the right answer. Because “man” is the complement (direct object) of “saw,” it cannot be the subject of “wrote.” The only other possibility is “who,” the correct answer.
     The last thing that we might note here is the effectiveness of the sequence for finding the type of a complete as compared to the traditional list of “linking verbs.” “Groaned” has never, to my knowledge, been included in a list of such verbs, but in Mary Renault’s The King Must Die, students will find the sentence “The gate groaned open.” By using the KISS sequence, it is easy to see that “open” is a predicate adjective because it describes the final state of the gate. 
Note! Especially in the early grades, KISS includes some exercises devoted specifically to the identification of predicate adjectives, predicate nouns, and indirect and direct objects. They are provided for people who may want or need them, but you will be doing you and your students a favor if you start with the exercises on “mixed” complements. The “mixed” exercises will more or less force students into using the sequence for determining the types of complements. You may not need to use the exercises on specific types of complements.
Adjectives and Adverbs

     Some textbooks spend a fair amount of time and space defining and describing adjectives and especially adverbs. But not all adverbs end in “-ly,” and some adjectives do (“friendly”). KISS focuses on the functions of words within a sentence. Thus: 

If a word describes a noun or pronoun, it is an adjective. 
If a word describes a verb, adjective, or another adverb, it is an adverb.
This explanation can be found in many textbooks, but it often gets lost in a mass of other material. Note that if students learn to identify adjectives and adverbs in this way, they will have little trouble in adapting the method to the prepositional phrases, subordinate clauses, verbals, and other constructions that function as adjectives and/or adverbs. (See the essay on “Nexus and Modification.”)

KISS Level Two - Expanding the Basics

Phrasal Verbs, the Importance of Meaning, and Alternative Explanations 

     I love the sentence “Put on your thinking cap!” in part because it demonstrated to me that many grammarians, including those who write textbooks, don’t think. In English, many verbs are actually phrases with words that look like prepositions at the end of them -- “put on.” Grammarians give these verbs a variety of names, of which “phrasal verbs” is one. The grammarians, however, don’t try to teach students to use their knowledge of grammar to analyze real texts. Instead, they “discuss” grammatical terms.
     When I used this sentence as an example, I noted that students need to think about the meaning of the sentence. I did so because if you ask students to put parentheses around prepositional phrases, many students will unthinkingly place parentheses around “on your thinking cap.” The sentence, however, does not mean to place something “on your ... cap.” It means to place your thinking cap on your head.
     The grammar teachers to whom I was writing, however, ignored the problem of teaching students, and instead debated the various terms for describing such verbs and whether or not specific verbs are, or are not, phrasal. Thus one teacher said that “put on” is one because it can be replaced by “donned.” (What fourth grader will think of “donned” as a substitute for “put on”?) KISS method should stress the meanings of sentences, and it should allow alternative explanations.
     Some grammarians, for example, consider “look at” as a “must be” phrasal verb, whereas other grammarians consider it to be a verb “look,” plus a preposition. Because grammarians disagree, KISS allows alternative explanations. For example, in a sentence such as “They were looking at the doggie in the window,” KISS allows students to explain “look at” as the verb, and “doggie” as its direct object, or to explain “look” as the verb and “at the doggie” as a prepositional phrase. Note how this example differs from “put on” in that either explanation reflects the meaning of the sentence. 

Distinguishing Finite Verbs from Verbals

     Verbals are verbs that function as nouns, adjectives or adverbs. In order to identify clauses, students need to learn to distinguish verbals from finite verbs -- the verbs that form clauses. I am unaware of any pedagogical grammars that even attempt to enable students to do this, perhaps because “finite verbs” are almost impossible to define to people who do not understand grammatical tense and person. Here again, therefore, more (the term “verbal”) is actually less complicated and process (method) is important. To teach students to distinguish finite verbs from verbals, make them learn the three “tests”: 

1. The Noun Test -- A verb that functions as a noun (a subject, a complement, or the object of a preposition) is not a finite verb. (Do not underline it twice.)
2. The ‘To” Test -- A finite verb phrase cannot begin with “to.” Thus in “Bob went to his room to do his homework,” “to do” is not a finite verb. (Do not underline it twice.)
3. The Sentence Test -- If you are not sure about whether or not to underline a verb twice:
a. Find the subject of that verb.
b. Make a simple sentence using that subject and verb --without adding any words, and without changing the form or meaning of the verb.
c. If the sentence does not seem to be an acceptable sentence, the verb is not finite.
Remember that the details of verbals are the focus of KISS Level Four. Here, your objective is simply to enable students to know which verbs to underline twice and which not to. It will take a little practice, but the tests almost always work. 

KISS Level Three - Clauses (Subordinate and Main) 
KISS Level 3.1 - The Basics of Clauses

The Definition of a Clause

     A clause is a subject / finite verb / complement pattern and all the words that chunk to it. Make students memorize and use that definition. There are no exceptions to it. Any part of a clause can be compounded, and, as you will see if you examine random sentences, subjects, verbs, and/or complements can all be ellipsed (left out). But for students who have learned to identify S/V/C patterns, clauses are relatively easy to master if they use the definition and another method—another  Boolean sequence.
    Always have students analyze sentences systematically. Prepositional phrases first, then S/V/C patterns. Because a clause is an S/V/C pattern and all the words that chunk to it, there will be one clause for every such pattern. If there is only one pattern in a sentence, have students simply put a vertical line | after it.

Identifying Clauses

     KISS introduces the term “clause” in KISS Level Three with exercises on compound main clauses. You will find exercises on compound main clauses in many different sections of the KISS materials--for an interesting reason. Students’ inability to sense main clause boundaries results in three of the most discussed punctuation errors -- comma-splices, run-ons, and fragments. And most of these errors reflect thought on the students’ part -- and failure in current instruction. These errors often result from the students’ sense that there is a logical relationship between the two sentences that are spliced or run together. (A “comma-splice” denotes joining two main clauses with just a comma; a “run-on” denotes running one main clause into another with no punctuation that separates them.) Most traditional instruction tends to tell students to “fix” their errors by using a period and a capital letter. Doing so, however, hides the very logic that resulted in the error. In most cases, these errors are better fixed with a semicolon, colon, or dash. Thus KISS starts with compound main clauses AND the logic behind their being compounded.
     Once students get a general sense of compound main clauses, KISS introduces the subordinate clauses. The grade-level book for third grade introduces students to compound main clauses, and then to subordinate (noun) clauses that function as direct objects. The latter is simply because these students read and write so many sentences of the type “He thought [subordinate clause]” and “Mary said [subordinate clause]” As always, KISS attempts to introduce constructions in terms of their frequency, thereby enabling students to analyze of much of real texts as possible.
     Here we come to a point where the teachers’ art is extremely important. Our objective is to enable students to explain the clause structure of as many real sentences as possible. Teachers need to decide whether they want a long, slow learning curve, or a short fast one. The curve, moreover, has two slopes -- students have to determine the type of each subordinate clause (noun, adjective, adverb), and they also need to learn how to untangle sentences that have subordinate clauses within subordinate clauses that are within subordinate clauses, etc.
     The method for identifying clauses is relatively simple: 

1. If a sentence has only one S/V/C pattern, put a vertical line after it and go on to the next sentence. 
2. If a sentence has more than one S/V/C pattern:
A. Check for subordinate conjunctions. 
B. Start with the last S/V/C pattern and work backwards.
The instructional materials include a list of words that can function as subordinating conjunctions.

Distinguishing the Types of Clauses 

     In the KISS Approach, clauses, like almost every other construction, are distinguished by their functions. Consider, for example, the sentence 

Kara saw John playing soccer in the park where she was playing baseball with her friends.
Because students are expected to learn how to distinguish finite verbs from verbals in KISS Level 2.1.6, they should realize that “John playing soccer” is not a finite verb, and thus this sentence has only two S/V/C patterns: 
Kara saw John (DO) playing soccer in the park where she was playing baseball (DO) with her friends.
If they follow the procedure, students should recognize “where” as a subordinating conjunction. Thus “where” will be the first word in a subordinate clause. If students are paying attention to meaning (which is a major aspect of the procedures), they should also realize that “with her friends” goes with “was playing.” Thus (even if they do not recognize “with their friends” as a prepositional phrase) they should see that the last word in this clause is “friends.” Therefore they should put an opening bracket before “where” and a closing bracket after “friends.” In this sentence, the cKara saw John (DO) playing soccer in the park where she was playing baseball (DO) with her friends.lause further identifies, and therefore chunks to “park.” Because “park” is a noun, the clause is adjectival.
     Note that if the sentence were “Kara saw John playing soccer where she was playing baseball with her friends,” the “where” clause would chunk to “saw” and/or “playing” and thus function as an adverb.
     Again applying the definition of a clause, the first word of the “Kara” clause is “Kara,” and the last word, since the “where” clause chunks to “park,” is “friends.” And since every sentence must have at least one main clause, this must be it. A vertical line after “friends” thus completes the analysis of clauses in this sentence. Learning and applying the procedure will enable the students, with some practice, to identify adverbial, adjectival, and the various types of noun clauses.
     The question for teachers here is “Should you start with separate exercises on the various types of clauses (adverbial, etc.), or should you start with mixed exercises--exercises that include all three types of clauses. In the grade-level books, KISS presents a group of mixed exercises first. These are followed by groups of exercises on the various types of clauses, should your students need them.

Untangling Embedded Clauses

     The other slope of the curve is learning to untangle embedded clauses. Consider the following sentence, written by a fourth grader: 

I was putting the bacon (DO) in the microwave [when my sister asked Alice (IO) and me (IO) [how high she should put the eggs (DO) on]]. |
Beginning at the end of the sentence, the “how” clause functions as the direct object of “asked,” and is therefore part of the “sister asked” clause. The “when” clause functions as an adverb to “was putting,” and “I was putting bacon” is the S/V/C pattern of the main clause.
     Students will need some practice with untangling clauses like these. In the instructional books, you will find a group of exercises on these placed before the group on additional noun clauses, simply because embedded clauses are more frequent than are clauses that function as subjects, predicate nouns, or objects of prepositions. (Exercises on noun clauses used as direct objects--perhaps the most frequent use of subordinate clauses--immediately follow the group of mixed clauses.)
     Remember that the grade-level workbooks are intended as an example of how KISS can be taught and for your convenience. If you are working on clauses with fourth graders, you might want to ignore the workbooks and use the set of nineteen sample essays written by fourth graders. The instructional materials and the procedures will still work, students can learn to recognize clauses simply from the texts of their peers, and you can expect them to make mistakes with the “Advanced Questions.”

KISS Level 3.2 - Advanced Questions about Clauses

     The “Advanced Questions” probably involve less than five percent of the clauses you will find in randomly chosen texts. Teachers should probably browse the instructional materials and a few examples of these, but they should focus on Level 3.2 only after students have a fairly firm mastery of Level 3.1. The grade-level books do introduce the “So/For” (Level 3.2.2) question in grade four, simply because many of the stories third and fourth graders read include “for” as a conjunction. Note also that in the grade level books, fourth grade is basically devoted to KISS Level 3.1, and fifth grade to KISS Level 3.2.
     There are, it should be noted, some clauses that students should not be expected to be able to explain in KISS Level Three. These are primarily subordinate clauses that function as retained complements, as delayed subjects, or as appositives. The reason here is that all three of these types depend on an understanding of KISS Level Five constructions. (See KISS Level Five, below.) 

KISS Level Four - Verbals (Gerunds, Gerundives, and Infinitives)

     In KISS Level 2.1.6, students learn to distinguish finite verbs from verbals so that they will not underline verbals twice. The remaining instruction in verbals (understanding the three types, their subjects, and their functions) is left to KISS Level Four because an understanding of clauses is more important than an understanding of verbals. Note also that if students cannot recognize finite verbs, they will try to explain them as verbals.
     Learning to distinguish the types of verbals is a little complex in that students need to recognize verb forms, especially “participles.” Although some participles are irregular, most end in “-ing” or “-ed.” Gerunds and gerundives are participial in form; infinitives are usually not so. Learning this distinction will take some practice, but here again procedure is important. Having identified a verbal, students should follow this analytical sequence: 

1. Look for gerunds first. Gerunds always function as nouns. 
2. Any participle that is not a gerund is probably a gerundive. Gerundives function as adjectives
3. Any verbal that is not a gerund or gerundive has to be an infinitive. There is no other option. Infinitives can function as nouns, adjectives, or adverbs.
This procedure eliminates the cumbersome (and often incomprehensible to students) definition of an “infinitive.” Many, but not all infinitives can be identified by the “to” that marks them, and some tenses of infinitives end with participles. You will find, however, that these tenses appear relatively infrequently. 
     Another important part of instruction here is the exercises you use to teach students to identify the various verbals. As always, KISS presents a section on “Mixed Verbals” first. If the students use the procedure just described, they should be able to learn to identify the types and functions of almost any verbal in any text fairly quickly -- without a special focus on gerunds, gerundives, or infinitives. The students, after all, already know the functions. Gerunds can function in any what that a noun can (subject, direct object, etc.) Gerundives always function as adjectives, and infinitives can function as adjectives, adverbs, or in any way that a noun can. True, they can also function as interjections, but students who have learned to identify interjections should even be able to realize when an infinitive is functioning as an interjection.
     The section on mixed verbals is followed by sections that focus on gerunds, on gerundives, and finally, on infinitives, and these three sections include two or three exercises that do focus on identification, just in case you feel that your students need them. In most cases, I suggest you skip the ID exercises, but these three sections also contain exercises on style, logic, sentence-combining, and punctuation which you may want to use.
     The sections on infinitives are the longest, with eleven exercises, the first three of which are devoted to mixed exercises on infinitives. Of the three types of verbals,, infinitives have the widest range of functions -- subjects, predicate adjectives, predicate nouns, direct objects, objects of prepositions, appositives, interjections, delayed subjects, and, of course, adjectives, and adverbs. There is also the question of ellipsed infinitives, as in “They made Judy president.” You may want to have your students do the mixed exercises, but be frugal (of time and energy) in determining to use all the exercises in this section.

KISS Level Five - Noun Absolutes and Seven Other Constructions

     KISS Level Five was originally designed as a “mop-up” operation that includes eight constructions. If you are trying to teach KISS in a single year, you will almost certainly not be able to do a good job and include these constructions. But if you spread KISS across several years, you can include many of these constructions earlier in the instructional sequence. Indeed, the noun absolute is the only construction that must remain at KISS Level Five--the end of instruction. That is because the noun absolute is a noun plus gerundive (KISS Level Four) construction. If you try to teach noun absolutes before students can recognize gerundives, you will confuse many of your students. Note that throughout the KISS Approach, instruction is cumulative, and students should always be expected to identify prepositional phrases, S/V/C patterns, clauses, and then verbals. They will recognize verbals because they are the verbs that the students have not underlined twice. They will recognize many noun absolutes because they are a noun plus gerundive construction that they have not chunked to the rest of the sentence, as in “Yet here she was now, her pale profile outlined against the moonlight.”
     When and if you want to introduce the other seven constructions depends on your objectives and how much time you want to spend on grammar each year. In the grade-level books, simple interjections, nouns used as adverbs, and direct address are introduced in grade three, primarily because they are relatively easy to understand and because they appear frequently in the reading and writing of primary school students. Delayed Subjects and Passive Voice (including retained complements) are introduced in grade five. In part, the objective here was to introduce passive voice as early as possible because passive voice is an important stylistic question. The last of the eight, appositives, and post-positioned adjectives, are introduced in grade six, although they could probably be introduced earlier if students have a good command of subordinate clauses.
     Throughout this essay, I have tried to suggest the importance of method both for the students, who need to learn how to identify constructions, and for teachers, who need to think about the sequence in which they expect students to learn. To expect students to understand “B” (clauses) without having given them the ability to identify “A” (S/V/C patterns) will simply confuse and frustrate them. But perhaps more significantly, emphasizing “method” repeatedly and in different contexts impresses on students the most important characteristics of “strong,” “growth-mindset” people. In teaching KISS, you are not just teaching grammar. You are teaching students how to think better.