Presentation on theme: "Tell a person that they can think, and they will love you. Make a person think, and they will hate you. -Source unknown."— Presentation transcript:
Tell a person that they can think, and they will love you. Make a person think, and they will hate you. -Source unknown
What makes a good analytical thinker? Analytical thinkers not only make good scientists and engineers; analytical thinking makes people good responsible citizens, good workers, and, most important for you, good students. This presentation was prepared by Dr. Ed. Vavra, developer of the KISS Approach to teaching grammar. KISS ApproachKISS Approach
Blueprint for Educational Change In 1993, Dr. Arthur Whimbey, Dr. Mary H. Johnson, Dr. Eugene Williams, Sr., and Dr. Myra J. Linden published a book titled Blueprint for Educational Change ( The Right Combination, Inc.) This book should be much better known than it is!
Blueprint for Educational Change A major objective of the authors was to determine the differences between “strong” and “weak” analytical thinkers. They arrived at two major differences.
Blueprint for Educational Change 1.Strong thinkers are very concerned with details; weak thinkers are not. 2. Strong thinkers break any problem down into steps—they learn to use an analytical process; weak thinkers give one-shot answers, as if either one knows the answer or one does not.
The Nature of Analytical Ability In Chapter Two of the book, they give a number of questions from a 38-question test—the Whimbey Analytical Skills Index. The test was given to 500 students entering community colleges in New Jersey. This presentation is based on four of those questions and the results from the 500 students.
About this Presentation The authors make extremely perceptive (and very helpful) observations about how students answered the questions.
About this Presentation Because those observations are so important, and so clearly explained, the text in most of the following is quoted from pages 6 through 15 of the book. (My comments will be in light blue.)
Question 1 Which letter is as far away from K in the alphabet as J is from G? a. Kb. Mc. Nd. Ge. I
About Question # 1 Question 1 is fairly easy. However, to answer it correctly, a person must carefully read it and perform several mental operations. Quoted from page 6.
About Question # 1 Research shows that good analytical thinkers often read the question in parts, talking to themselves and rephrasing ideas in their own words to help grasp the ideas completely. They may read the entire problem through to get an overall picture, and then reread it in sections—something like this: Quoted from page 6.
About Question # 1 “Which letter is as far away from K—I have to find a letter that is some distance from K—in the alphabet as J is from G. OK, I need to get the distance from J to G. Then, if I count that same distance off from K, I should have the answer.” Quoted from page 6.
About Question # 1 The best answer from among the alternatives offered is N (alternative c).... Seventy-seven percent of the students answered this question correctly. But 23% did not. Apparently the latter students had not learned how to accurately read through a problem such as this and then go through the necessary steps to reach the correct answer. Quoted from pages 6 and 8
About Question # 1 Incidentally, research on reasoning has revealed many myths about mental skills. For example, did you count on your fingers in solving this problem? Quoted from page 8
About Question # 1 After conducting workshops on reasoning, we have been told by teachers that they counted on their fingers but did it clandestinely under books or desks. Several even admitted they counted with their hands in their pockets to avoid embarrassment--to conceal this hidden activity. Quoted from page 8
About Question # 1 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. Quoted from page 8
About Question # 1 However, when a group of mathematics and science teachers was asked to solve this problem, a number of them also counted on their fingers. Some even wrote out a portion of the alphabet to count off the letters in reaching their answer. Quoted from page 8
About Question # 1 Rather than being a sign of immaturity, such activities reflect a strong concern for accuracy in processing information. Research shows that a major difference between strong and weak analytical thinkers is that strong thinkers have a much greater concern for accuracy, and they tend to engage in more activities to insure accuracy in solving problems. Quoted from page 8
About Question # 1 This will be discussed again with later problems. For now, suffice it to say that peripheral activities like finger counting are good not bad practices in problem solving. They are part of actively and accurately processing information. Quoted from page 8
About Question # 1 Finally, although answer N (alternative c) is the correct choice, some good thinkers initially conclude that the letter H should be the answer. The problem asks you to find a letter which is “as far away from K... as J is from G.” H is the same distance from K as J is from G. Quoted from page 8
About Question # 1 When good thinkers notice this, they reread the problem and see it does not specify direction—only distance. They then try counting off the distance from K in the other direction, and arrive at N. Quoted from page 9
About Question # 1 What’s interesting about this solution is that it represents in miniature the way analytical thinkers often deal with real-life problems. If, after obtaining some information about a problem, they find they cannot arrive at a solution, they go back to the problem and examine it again to look for more information or a different perspective. Quoted from page 9
About Question # 1 In fact, this also replicates in miniature what is called the scientific method, in which an investigator makes some observations, formulates an hypothesis, makes some more observations to see if the hypothesis is correct, and changes the hypothesis as required by additional new data. Quoted from page 9
About Question # 1 This illustrates why scientists tend to score well on tests of analytical ability. Such tests measure the cognitive habit needed to pursue science. Quoted from page 9, my emphasis
A Comment about Question # 1 Making notes and counting on one’s fingers are to math what detailed brainstorming is to writing. A good paper is written from the bottom (details) up. As Ben Franklin said, “An empty sack cannot stand upright.” (EV)
A Comment about Question # 1 The examples (details) arrived at through brainstorming give a writer interesting and meaningful things to say. But weak writers refuse to brainstorm. It is not that they can’t. Most often, they just do not want to take the required time. (EV)
Question # 2 There are 3 separate, equal-size boxes, and inside each box there are 2 separate small boxes, and inside each of the small boxes there are 4 even smaller boxes. How many boxes are there altogether? a. 24b. 13c. 21d. 33 e. some other number
About Question # 2 Question 2 can be solved most readily by making a diagram such as in Figure 2, showing that the answer is 33. Quoted from page 9
About Question # 2 This question also reveals a common myth about reasoning. When a group of math and science teachers tried solving it, several asked apologetically whether they were permitted to make a diagram. They explained that they could “see” problems like this better if they first drew a picture. Quoted from page 9
About Question # 2 The fact that these experienced math and science teachers meekly asked whether they could make a diagram reflects the common misbelief that good thinkers can solve all problems mentally, that only poor thinkers must resort to scratch paper and diagrams. Often quite the opposite is true. Quoted from page 9
About Question # 2 Many mathematicians think with a pencil in their hand to make diagrams and computations. It improves their understanding of problems and their accuracy. Quoted from page 10
About Question # 2 In contrast to this, high school physics teachers have reported that they often cannot get weak students to make diagrams in solving problems, even when diagrams are useful or necessary. Quoted from page 10
About Question # 2 Weak students tend to be one-shot thinkers. They habitually skim through a question and then jump to an answer. They have not learned to work step-by-step through a problem, spelling out all the details and making diagrams as needed, until they understand the information fully in coming to an answer. Quoted from page 10, my emphasis
About Question # 2 The common myth that good thinkers are purely cerebral, that they can do everything mentally and do not require diagrams, reinforces the poor thinking habits of analytically weak students. Quoted from page 10
About Question # 2 In the New Jersey Task Force study, only 37% of the students answered this question correctly. The most common incorrect answer given by weak students is 24. They just take the three numbers in the problem (3, 2, 4) and multiply, without first spelling out the information in a mental picture or a diagram to see whether this multiplication is appropriate. Quoted from page 10
A Comment about Question # 2 Note that diagrams are to math problems what outlines are to writing. Weak writers regularly tell me that they don’t like to make outlines. It is not that they can’t; they just do not want to. (Is this because making an outline requires thinking about what one is going to say?) --EV
Question # 3 Ten full crates of walnuts weigh 410 lb, while an empty crate weighs 10 lb. How much do the walnuts alone weigh? a. 400 lbb. 390 lbc. 310 lb d. 320 lbe. 420 lb
About Question # 3 Question 3 is fairly easy, but it must be read and thought through carefully in order to carry out appropriate arithmetic operations. Quoted from page 10 [54% of the students had the correct answer. – EV]
About Question # 3 Although the correct answer is 310, the most common incorrect answer is 400.This answer is easy to rationalize: The person has subtracted the weight of only one crate instead of 10. Quoted from page 10
About Question # 3 Still, it is symptomatic of the cognitive style underlying low analytical ability. Weak analytical reasoners tend to skim through a problem and quickly jump to an answer, frequently with the attitude that you either know the answer to a problem, or you might as well give up and guess. Quoted from pages 10 and 11
About Question # 3 Some weak students answer 420 for Question 3. This answer is more difficult to rationalize, since it says that the walnuts alone weigh more that the crates and walnuts combined. Students who give this answer are the type who sometimes tell math teachers they can do math but just can’t solve word problems. What they mean is they can do simple arithmetic but cannot analyze a problem to see what arithmetic operations are needed. Quoted from page 11
About Question # 3 I’ll interject here to note that the question includes a subordinate clause—“while an empty crate weighs 10 lb.” In Trevor J. Gambell’s “What High School Teachers Have to Say about Student Writing and Language across the Curriculum” (English Journal, September 1984), he states, “Teachers... found problems with texts which employed multiple choice questions with subordinate clauses. Students had difficulty determining the main idea of the sentence and thus the question; the subordinate clause led to ambiguity and confusion.” ( 43) Rather than suggesting that students should be taught how to understand subordinate clauses, he concluded, “This problem also warns us that multiple choice questions need to be worded as simple sentences so that content is being tested rather than language.” And this was in English Journal, the main publication for high school English teachers!? (EV)
About Question # 3 To solve this problem, one must read it carefully and fully conceptualize the information, namely that the total 410 pounds is made up of two parts, walnuts and crates, and that the crate weight has 10 components, as shown in Figure 3. Quoted from page 11
About Question # 3 Computationally, there is more than one way to solve this problem. One can figure that since there are 10 crates, and each crate weighs 10 pounds, the total crate weight is 100 pounds. This is then subtracted from the total poundage to get the weight of the walnuts. 410 -100 310 Quoted from page 12
About Question # 3 Another way to solve the problem is to figure that if 10 full crates weigh 410 pounds, then one full crate weighs 41 pounds. Since the crate itself weighs 10 pounds, the walnuts inside one crate weigh 31 pounds. Therefore the walnuts inside 10 crates weigh: 31 x10 310 Quoted from page 12
About Question # 3 While these two solutions are computationally different, they are both based on an accurate mental representation of the information in the problem. Low-ability students must learn to construct such accurate mental representations. Quoted from page 12
Question # 4 Cross out the letter after the letter in the word “pardon” which is in the same position in the word as it is in the alphabet.
About Question # 4 Question 4 looks a bit like IRS tax instructions. But it also looks like the complicated sentences found in law books and textbooks in chemistry, physics, economics and other scholarly fields. Quoted from page 12
About Question # 4 For example, here is a sentence from a text on language usage. When a compound modifier begins with a word ending in -ly or follows the word it modifies, there is no need for a hyphen. Quoted from page 12
About Question # 4 If you are not already familiar with this rule, if you have to read the sentence carefully to see exactly what it means, you find yourself going through the same type of step-by-step mental gymnastics that you use in answering Question 4. Quoted from page 12
About Question # 4 In other words, Question 4 does not involve just some trivial test gamesmanship. It taps the same mental ability needed to comprehend complicated material encountered in all advanced academic subjects. Quoted from pages 12 and 13
About Question # 4 An analytically strong student was asked to think aloud as he solved Question 4, to see the mental steps he used. Here is his response: Quoted from page 13
About Question # 4 Cross out the letter after the letter in the word “pardon.” That’s confusing; I’ll read it again. Cross out the letter after the letter in the word “pardon.” I guess I have to cross out some letter in “pardon,” but I’m still a little confused. I’ll read the rest of the problem and see if that helps. Quoted from page 13
About Question # 4...which is in the same position in the word as in the alphabet. I guess the word being referred to is “pardon.” Quoted from page 13
About Question # 4 It says, “same position in the word.” What do I mean by “same position in the word”? Quoted from page 13 [Note how “What do I mean” shows the student taking meaningful possession of the question. Weak students rarely do this; instead they just give up. (EV)]
About Question # 4 Well what does “position in the word” mean? Let me look at the word “pardon.” I guess “p” is in the first position in “pardon”; “a” is in the second position; “r” is in the third position. Quoted from page 13
About Question # 4 In the alphabet, “a” is in the first position, “b” in the second, “c” in the third. I need to find a letter which is in the same position in “pardon” as in the alphabet. Quoted from page 13
About Question # 4 Looking at the word “pardon,” “p” is in the first position in “pardon,” but “p” is not in the first position of the alphabet; “a” is in the second position in “pardon,” but it isn't in the second position of the alphabet; “r” is in the third position in “pardon,” but not in the alphabet; “d” is in the fourth position in “pardon.” It is also in the fourth position of the alphabet. Quoted from pages 13 and 14
About Question # 4 So I have pinned down the letter “d.” But there was something at the beginning of the problem that confused me. Let me reread the beginning. Quoted from pages 13 and 14
About Question # 4 Cross out the letter after the letter in “pardon.” So I have to cross out the letter after the “d” in “pardon.” That is the “o.” I’ll cross out the “o.” Quoted from page 14
About Question # 4 This solution is particularly interesting because when nonanalytical students miss Question 4 and are asked to explain their difficulty, they often say they did not know what “same position in the word as in the alphabet” meant. The analytical student above did not initially understand this phrase either. Quoted from page 14
About Question # 4 But having an analytical habit of mind, he broke it down by first figuring out what was meant by “position in the word.” Once he understood that, he was able to figure out what was meant by “same position in the word as in the alphabet.” Quoted from page 14
About Question # 4 This highlights a major difference between strong and weak analytical thinkers. Strong analytical thinkers engage in more of the minute mental activities that lead to comprehension. They have learned how to construct meaning for themselves. Quoted from page 14
About Question # 4 Weak analytical thinkers tend to be less active in pinpointing precise meaning. They have not learned how to break down complex parcels of information into manageable parts by starting with something they can understand and building from there. Quoted from page 14
About Question # 4 Strong thinkers are more active in this regard. They have a greater tendency to talk to themselves at length while solving a problem – asking themselves questions, answering the questions, and rephrasing ideas into their own words. Quoted from page 14
About Question # 4 They work step-by-step, stopping to figure things out and pin down exactly what everything means. In short, they do more analytical processing. Quoted from pages 14 and 15
About Question # 4 People critical of tests point out that Question 4 can be rewritten so it is easier to comprehend. This is true. Here is a simpler version: Cross out the “o” in “pardon.” Quoted from page 15
About Question # 4 However, psychometricians include questions like 4 on tests because such questions distinguish analytical from nonanalytical students. While Question 4 can be written more simply, advanced chemistry, physics and mathematics textbooks cannot be rewritten in a way that makes them accessible to nonanalytical students. Quoted from page 15
About Question # 4 A great deal of research has been invested in trying to make textbooks more readable. Vocabulary and sentence structure can sometimes be simplified. But there is a limit to how simple physics and chemistry textbooks can be made. Their difficulty lies in the complexity of the ideas, not in the structure of the language. Quoted from page 15
About Question # 4 Question 4 has been written in an intentionally complex manner so that it taps the same analytical skill required to comprehend advanced academic material. Quoted from page 15
About Question # 4 In the study of these questions by the New Jersey Task Force on Thinking, Question 4 proved to be the most difficult: Only 33% of the students answered it correctly. What is remarkable is that Question 4 does not require any creative insights or cognitive leaps. It only requires that a student work step-by-step through the problem to pin down exactly what it says. Apparently, this is a mental skill which many high school students have not mastered. Quoted from page 15
Quiz On a piece of paper with your name on it, answer the following question: What are the two major differences between “strong” and “weak” analytical thinkers?
Conclusion The two major differences between “strong” and “weak” students are that: 1. “Strong” students break problems down into smaller ones and work their way through them, step-by-step. “Weak” students take the attitude that either one knows the answer or one does not. (EV)
Conclusion 2. “Strong” students are concerned with details. They make diagrams and notes when appropriate to help them understand the questions. “Weak” students won’t take the time to do that. (EV)
Conclusion Note that both of these differences are matters of habit, attitude, and willingness to put in time and work. If you are currently a “weak” student, you can train yourself to be stronger. (EV)
Just for Fun A genius is someone who is screwed up in a useful way. A grownup is someone who suffers from responsibility. Good Health is merely the slowest possible rate at which one can die. I chose the path less traveled, but only because I was lost. Work when you should and play all the time. Not he, who has much, is rich... but he, who gives much. One must wait until evening to see how splendid the day has been.
A Note about Art Whimbey I corresponded with Art Whimbey for several years. He generously gave me permission to make an electronic, interactive version of his Analyze, Organize, Write, an excellent book for students. (Unfortunately, the program doesn’t run on newer computers.) Dr. Whimbey sent me a copy of Blueprint, and to this day I still think that it is the most insightful book on what needs to be done to improve education. I also owe him a debt. In the course of our correspondence, he asked to see a manuscript that I had written about KISS grammar. The manuscript had lain in a drawer for fifteen years, but Dr. Whimbey’s enthusiasm about what I had written encouraged me to renew my efforts to develop the KISS Approach. For that, I sincerely thank him. Dr. Ed Vavra (July 11, 2011)
A Note about KISS Grammar Most grammar textbooks teach students what subjects and verbs are, but they do not even try to teach students how to identify the subjects and verbs in their own writing. Fourth grade teachers have told me that they are supposed to teach their students “clauses,” but many students can’t understand them. The reason they cannot understand clauses is that a clause is a subject/verb pattern (and all the words that go with it). If the students cannot identify subjects and verbs in their own writing, they will have major problems with clauses. This is only one of the numerous problems in the teaching of grammar that the sequential KISS Grammar Approach directly addresses. For more information about KISS, go to the KISS Grammar site at http://home.pct.edu/~evavra/KISS.htm, or search the web for “KISS Grammar.”http://home.pct.edu/~evavra/KISS.htm Dr. Ed Vavra (July 11, 2011)