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Circunferencia Ecuaci´ on de la circunferencia

In document Apunte UChile Introducción al Cálculo (página 43-58)

Teorema de pit´ agoras

2.3. Circunferencia Ecuaci´ on de la circunferencia

Meanwhile, the process of reading the AP tests continued to evolve with the vast growth of the program. In 1957, Valley suggested that local faculty hold most of the responsibility for grading, but by 1960, the sheer number of test takers ruled out that possibility. In March of 1961, Robert Jameson, Director of AP Reading, wrote an extensive report titled “Grading of the

College Board Advanced Placement Examinations” in which he outlined the entire grading process and the challenges inherent in such a young program. The report included five sections:

• The Grading Scale

• Setting and Maintaining Standards

• Weighting

• The Cut off of Grades for Reporting Scores to Colleges

• Miscellaneous Matters

At the launch of the program, the grading system was erratic, with each committee of readers “setting up its own system” of minimum scores, conversion of raw scores, depth of grading, and error-marking. Some groups decided on a maximum raw score of 24, and others made it possible for students to score up to a whopping 3,000 points on the raw score. With that many points to grade, however, the readers had to scrutinize every aspect of the composition – a time-consuming, impractical process. On the other hand, the lower raw score of 24 (or a similar number) did not allow the readers to produce a detailed, sustainable grade. Consequently, a “uniform system of grading” developed in the spring of 1957 and was incorporated into the program for the 1957 examinations (Jameson 1, 1961).

Jameson also made a critical distinction in grading that AP Readers still discuss today: the variations of a score, or “the many kinds of a 4” (Jameson, 1 1961). Some readers viewed the 1-5 scale as inadequate. They worried that most readers would avoid granting a “1” or a “5” because of the tendency to avoid extremes. However, Jameson outlined various ways that a student’s writing could earn a certain score, and so the 1-5 scale was defined, with layers, from 1-15 (as seen on the next page).

Table 9 1961 AP Scale

1961 Scale as defined for Readers: (Jameson 1961) 5

15 All three demonstrate unusual

competence, or mastery 14

13

The 15 = 5+; 14=5; 13=5-

4

12 All three demonstrate competence

11 10 3 9 8 7

All three suggest competence

2

6 5 4

All three suggest incompetence

1

3 2

All three demonstrate incompetence 1

0

The zero has various uses. In some examinations, it is automatically awarded only for a missing answer or a complete non sequitur. On the other hand, history readers award the zero to an answer which, while ostensibly on the topic, is so empty as to be considered worse than a failure.

The English Literature and Composition exam of 1960 was the only test graded with a slight variation. Instead of scoring the eight answers from 1-15, graders looked at question #1 and then “prepared a list of legitimate statements which might be made on each question. Each answer was then given the number of points it earned” and, graders added and converted those scores to the 15-point scale (Jameson 3, 1961). Contemporary AP English tests contain three essay questions scored on a 1-9 scale, but the mantra of AP trainers remains similar: “there are many rooms in the house of 6” (adage within the AP readers’ community). It can be difficult to realize that good writing comes in many forms and “voices.” One student may have exceptional command of the language but may lack in grammar. Another may write beautiful prose but then could misread a prompt. The need for the detailed statements makes sense, especially for an accurate evaluation of eight questions.

AP tests that contained both objective (multiple choice) questions and essay prompts had to be weighted in an equitable, logical manner. According to Jameson’s 1961 report, the

examination committee determined the weights based on three factors: 1. The time allotted to each section and to each question;

2. The importance, in the opinion of the committee, of one section of the essay section as against another in defining qualities of performance in areas of particular significance for advanced placement students;

3. The coverage of the objective section in comparison with that of the essay section. The 1961 English Examination contained “three essays, of equal final value, except that the grade on I and the literature grade on III made up the literature mark reported to the colleges; the grade on II and the writing grade on III made up the composition grade reported to colleges” (Jameson 7, 1961). Because there was only one English exam at the time, the test questions had to be divided into two categories: Composition and Literature. Thus, essay #III appears to count for twice as much as the other two because of its literature and composition points. The English sub-scores resembled the history sub-scores, presented on the following page:

Figure 2 English Sub-Scores

1960 American History

Objective Section – 25% Essay Section – 75%

In the Essay Section:

Part I (25 minutes) – 15%

Part II (two questions, total of 1 hour 40 minutes) – 60%

Each Question in the Essay Section:

Presentation and Mechanics – Weight 1

Facts – Weight 2

Generalization, Interpretation – Weight 3

Thus, for each question, in final scoring (essay section) the raw score for facts and for generalization are multiplied by factors which give the proper weights:

Presentation & Mechanics: 15 (max) times 1=15 Facts: 15 (max) times 2=30 Generalization/Interpretation: 15 (max) times 3=45

Maximum Raw Score: 90 (Jameson 7, 1961)

Jameson also noted that the weighting of sub-parts would differ from year to year

grading system. Today, the objective section of the English tests counts for 45% and the essays for 55%. Graders employ a scale of 1-9, and in place of sub-categories, they use a detailed rubric for each awarded score. In his report, Jameson recognized those scholars who thought that evaluating the essays on a three-point scale would expedite the grading process. While it would make the process seem faster, he asserted that the “haziness” of such a broad scale would be a cause of dissention among graders and would ultimately make it more difficult to come to an agreement. Also, with only three groups, (the top getting AP placement, the middle taking regular freshman English, and the bottom taking a remedial English course), students would inevitably find themselves placed in the wrong category. Although the 15-point sub-scores might have seemed complicated to some, he assured participants that the sub-scores were “something a reading committee can be taught to get hold of and use ….confidently” (11). As someone who has graded many AP essays, I agree wholeheartedly. In order to justify the grades I award, I must be able to back up each decision with a specific reason, and if I cannot do that, I am going to ultimately have to deal with confused students and dissatisfied parents who demand an accurate prediction of future AP test scores.

In the sixties and up to today, maintaining consistent standards for the examinations fell in large part to the Chief Reader, who had an active role in the testing process from the creation of the test to its administration. Upon construction of each question, the Chief Reader had the responsibility of organizing data for each answer (although the data varied in type depending on the subject: English data might include broad statements, whereas European History would require many pages of specific terms, dates, and events that would constitute the answers). Table leaders, first established in 1961 to assist the chief readers, have been an integral part of the reading process ever since. In sum, with many steps to ensure that the readers met the College

Board’s high standards, the actual “standards for grading [were] developed from the very beginning – from the committee meetings in the fall” (Jameson 5, 1961). For the current test, I do not have an issue with the way AP readers grade the English exam. In my experience, we “calibrate” our definition of a 1-5 score based on student samples, we familiarize ourselves with the prompt and with possible passing answers, and we grade holistically, looking for what “works” and not for what doesn’t. In other words, we do not take many points off for a missed comma or misspelling unless the grammatical error hinders the clarity of the paper. When I grade sample papers from the College Board, my grades reflect the grades given by the actual AP graders. Likewise, when my colleagues and I get together to discuss scoring methods, we usually find that we are “calibrated” together. If we do not agree on a grade for a paper, we discuss the reasons and adjust our philosophy accordingly.

In document Apunte UChile Introducción al Cálculo (página 43-58)

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