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SUPPLEMENTAL MATERIALS FOR STAND AND DELIVER


THESE SUPPLEMENTAL MATERIALS ARE BEING REORGANIZED AND ARE NOT COMPLETE.


   
TABLE OF CONTENTS

Notes for a short introduction to the movie.

Teaching opportunities described in this Learning Guide include: Additional Discussion Questions:
      Social-Emotional Learning
      Moral-Ethical Emphasis
            (Character Counts)

Additional Assignments

Other Sections:
      Bridges To Reading
      Links to the Internet
      Selected Awards & Cast
This film demonstrates that teenagers from disadvantaged backgrounds can accomplish amazing things when properly motivated and assisted by a good teacher. There is also strong evidence that twelve Garfield High students who passed the AP Calculus test in 1982 cheated on one problem: a question for which they all got the same wrong answer. It is clear that these students learned calculus and this fact does not undercut the message of the film. However, the evidence of cheating puts an interesting twist on the dispute with the ETS. It also provides an opportunity to teach students about due process in modern society and some of the problems with cheating. See teaching opportunities (5) and (6) below.

This Learning Guide explores teaching opportunities from "Stand and Deliver" in six areas:

  1. Lasting Change Takes Preparation to Achieve and Effort to Maintain
  2. Ideas Move Across Continents and Oceans
  3. We Can Get A Taste of Calculus in Finding the Area of a Circle
  4. Literary Devices in a Work of Historical Fiction
  5. Public Policy and Burdens of Proof in Modern Society (Perhaps the ETS Gave the Students a Break)
  6. Some Problems With Cheating

This Guide provides suggestions for teaching each unit, Notes for a Sample Introductory Lecture, student handouts, and comprehension tests. The units may be taught on their own or in conjunction with other units.

Mr. Escalante said, "Math is the great equalizer." Ask the class what he meant by that. Perhaps he meant that the logic of math is the same for all of us, no matter what our background is. Or perhaps he meant that if you can do math your skin color or surname don't matter. You can compete with anyone and get a job.



Helpful Background:

Lasting Change Takes Preparation to Achieve and Effort to Maintain: The Garfield High Mathematics Program

Jaime Escalante refused to accept the common "wisdom" that Latino kids from the barrio couldn't learn advanced math. He was not, like the head of the math department in the movie, beaten down by lack of resources, difficult students and an inability to inspire them. He believed that if he demanded high achievement and gave his students the right academic tools, they could do anything. To prove his point, Mr. Escalante fostered a team spirit in which the students worked together to beat the AP Calculus test.

Mr. Escalante worked for six years before the breakthrough 1982 test in which 18 Garfield High students demonstrated that they had mastered calculus. He started by encouraging area middle schools to offer algebra in their eighth and ninth grades to help students acquire the background necessary to understand calculus. He also convinced the schools to upgrade the standard of instruction. Mr. Escalante, supported by his principal, Peter Gradillas, also worked to impose higher standards in the pre-calculus classes offered at Garfield. He taught intensive math classes during the summer. Advanced Placement Calculus was offered to any student who wanted to attend and who would maintain the rigorous schedule set by Mr. Escalante.

The Garfield High math program was a great success. In the peak year of 1987, seventy-three students passed the test and another twelve passed a more advanced version given after a second year of calculus.

Some kids who participated in the Garfield High math program didn't take the AP Calculus test and some who took it didn't pass. However, the program raised standards and expectations for all students attending math classes at Garfield. College professors and administrators noticed that Garfield students who had been through Mr. Escalante's math program were better prepared for college than students who came from other schools in the area.

The achievements of Mr. Escalante's students have inspired teenagers all over the country to learn calculus. Many teachers have sought to emulate his teaching methods. Mr. Escalante was awarded the United States Presidential Medal. He was also given the Andres Bello award by the Organization of American States. In 1999 Mr. Escalante was inducted into the National Teachers Hall of Fame.

Unfortunately, Mr. Escalante's program does not presently exist at Garfield High. Mr. Gradillas, the principal who supported Mr. Escalante, left at the end of the 1987 school year to get a Ph.D. The new principal had other priorities. By 1991, frustrated by lack of administrative support and stymied by faculty politics, Mr. Escalante took a position in another high school. Despite the valiant efforts by his successor, the AP Calculus program had collapsed by 1996.

The Educational Testing Service has become an international institution, giving the Scholastic Aptitude Test (SAT), tests in specific subject matters, and advanced placement tests to millions of children each year. Scores on these tests determine the fate of applicants to colleges all over the United States.

Ideas Move Across Continents and Oceans: From Zero to "the Finger"

Zero:       The Maya were one of the greatest civilizations in pre-colonial America, occupying territory in southern Mexico, Guatemala, and Belize. They developed hieroglyphic writing and the concept of zero as a number to use in mathematical operations. They also invented place-value numbers, which are the only efficient way to denote large numbers and use them in mathematical computations. Hundreds of years before any other civilization, the Maya combined these concepts into an effective place-value computational system that used zero as a number.

By 1500 B.C.E. the Maya had settled in villages and employed agriculture to grow corn, beans and squash. They built large stone buildings, had pyramid temples, made paper from the bark of trees, and wrote in books. The Maya were excellent astronomers and they developed a calendar. The Maya worked metals such as gold and copper. At its height, the Mayan civilization had approximately 40 cities with populations from 5,000 to 50,000.

The classical period of Mayan civilization lasted from approximately 250 C.E. to 900 C.E. and declined for reasons that are not known. By the 16th century, when Europeans came to Central America, Mayan civilization had subsided into small agricultural villages.

The Maya used a base of 20 (from 10 fingers and 10 toes) grouped in sets of five (one for each hand and foot). Numbers were expressed in dots (for one), bars (for five) and a shell for zero.

Zero is not an easy concept. Mathematics started when people began counting objects, for example, cows, sheep, and jars of olive oil. It was practical and not theoretical. Ancient peoples (except for the Maya) had no concept of zero or of negative numbers. When the ancient Babylonians needed to start counting large numbers of objects, they developed the place-value system long before the Maya civilization existed. For a thousand years the Babylonians used a place-value system without a zero. 2106 would be written in the same way as 216. The Babylonians relied on the context in which the number was used to clarify which number they meant.

Our place-value, base ten numbering system works as follows. The term digit refers to an Arabic numeral (1,2,3,4,5,6,7,8,9 or 0) within a larger number. Thus the digit 5 appears twice in the number 1,345,561. The location of a digit within the number indicates the power of the base to which it relates. Because we use a base of 10, the digit not only refers to its own value but it is multiplied by the power of ten that corresponds to its position within the number. We start with the one's place. That is very straightforward, like counting on our fingers. The first place to the left is the ten's place (101). The digit in the ten's place is multiplied by 101 (i.e. 10) to determine how much it adds to the value of the number. Thus, the number 61 = one plus 6 X 101. The second place to the left of the one's place is the hundred's place (102). The digit in the hundred's place is multiplied by 102 (i.e. 100) to determine how much it adds to the value of the number. Thus, 561 = 1 + 6 X 101 plus 5 X 102. The digit in the million's place (106), which is the six places over from the one's place, adds its own value multiplied by 1,000,000 to the value of the number. Therefore the number 1,345,561 means 1 + 6 X 101 + 5 X 102 + 5 X 103 + 4 X 104 + 3 X 105 + 1 X 106.

The Babylonians used a base of 60 which serves the same purpose as the number 20 in the Mayan system and the number 10 in our system. After the Babylonians had counted to 59, they put a one in the next place to the left, the 60's place.

In about 400 B.C.E. the Babylonians began to use a slash mark to show that there was nothing in a particular place. 2016 would be written 2/16. Thus, they used the slash mark as a "place holder". This is one of the primary uses that we make of zero but the Babylonians didn't recognize that zero was itself a number that could be used in mathematical computations.

Greek mathematics (the Ancient Greek golden age began in the third century B.C.E.) was based on geometry which measures the length of lines. Geometry deals with positive numbers and doesn't need zero. Nor did the Greeks have place-value numbers even though they were more advanced than the Babylonians in many aspects of civilization. The Romans (5th century B.C.E. - 5th century C.E.) didn't have the zero either and even though Roman civilization was very advanced and flourished hundreds of years after the Babylonian civilization the Romans didn't use the place-value numbering system.

The first society other than the Maya to discover the concept of zero as both a place holder and a number for use in mathematical calculations were inhabitants of the Indian subcontinent in Asia. They developed a ten-based, place-value system using the antecedents of 1,2,3,4,5,6,7,8,9 & 0. By about 600 C.E., after several hundred years of development, these numbers were standard in India. Thus, the Indians treated zero as a number and used it in computation, at the same time as or a few hundred years after the Maya.

The Arabs from the Middle East would trade with these Indians. They saw how advanced the Indian numbering system was and they adopted it. Arabs refer to the numbers 0 - 9 as "Indian numbers." From the Middle East these concepts spread to Europe in the 11th century C.E. where the numbers 0 - 9 are called the "Arabic numbers." By this time the Mayan civilization had reached its peak and had been in decline for about two hundred years. The use of zero and the place-value system was gradually adopted throughout Europe from the 12th century to the Renaissance in the 14th century.

As the Mayan civilization declined, its mathematics was lost. Zero and the place-value numbering used by the modern day inhabitants of North and South America came back to the lands of the Maya with the Spaniards as they colonized the Americas.

The Finger:        [Before starting this section of the unit, ask the class, "Where did this gesture come from? How did it get to the Latino boy in Southern California who gives Mr. Escalante the finger?"]

Different hand signs mean different things in different cultures. For example the "thumbs up" sign means "good going" or "everything's OK" in the U.S. and many other places. However, in the Middle East, parts of West Africa, Russia, Australia and other places it is very derogatory. The "OK" sign formed by linking the thumb and the first finger to make a rough circle is accepted as a sign of approval in the U.S. and many other countries. However, in Latin America it is a gross insult, being the equivalent of calling someone an "a__ hole." In parts of Europe this means "nothing" and in Japan it means something like "give me change."

The extended middle finger has been an insulting gesture from the time of the ancient Greeks and Romans, and perhaps before. The first reference to "the finger" appears in a play called "The Clouds" written in 423 B.C.E. by the Greek dramatist Aristophanes. The play contains a scene in which a character has a debate with the great philosopher Socrates. The character gets a little angry and gives Socrates the finger.

The Romans adopted much of their culture from the Greeks. Roman sculpture is very much like Greek sculpture. The Roman gods are similar to the Greek gods. Much of Roman literature was based on Greek literature. The Romans also adopted some Greek obscenities. "The finger" was a well established Roman insult. They had two names for this gesture, the "digitus infamis," roughly translated as the "infamous finger" and the "digitus impudicus" meaning the "indecent finger."

Roman culture spread to Europe with the conquests of the Roman Empire. The Roman influence came to the U.S. through the European settlers along two pathways. European culture came directly to North America through colonization and also indirectly through emigration of Latino people from Central America and Mexico. Angel's friend could have inherited the gesture in either of these two ways. (He could have learned it from U.S. culture or it could have been part of his Latin American heritage.) In any case, the origins of "the finger" stretch back to ancient Greece some 2500 years ago.

Modern society has many things that are new, such as computers, the Internet, cars, airplanes, space travel, and electronic music. However, a lot of what we use or experience every day has come rather directly from ancient civilizations. A few of the thousands of examples are: Babylon: writing; the 60-minute hour; the 12 lunar months in a solar year; the city-state; a written legal code (Hamurabi); place-value numbers; ancient Israel: monotheism, morality-based religion; the Bible, the teachings of Jesus Christ; the concept of time as progressing forward rather than history not progressing at all or being cyclical; ancient Greece: geometry; philosophy; democracy; Olympic Games; classical sculpture; drama; ancient India: zero, Arabic numerals; ancient Rome: representative government (the Roman Senate); the balance of powers in government; the alphabet; Renaissance Europe: scientific method, humanistic outlook; Medieval England the concept of individual rights and limited government (from Magna Carta); the common law.

End this section of the Unit by telling the class that any time anyone gives them "the finger," that person is honoring an ancient Greek tradition that has traveled a long road over the centuries and over continents and oceans.


Suggestions for Using This Unit: This unit consists of a lecture after the movie based on the text of the Helpful Background section, supplemented with the teacher's own insights about the movement of knowledge, and followed by a Comprehension Test on the Movement of Ideas and a Taste of Calculus. This can be printed and distributed to a class or modified by the teacher for the needs of a specific class. In the alternative, the test can be used as a homework assignment.

For Social Studies curriculum standards for the eleven most populous states relating to the Movement of Ideas and the Maya, click Here.



For web sites on the Maya, see:

Sources for discussion of zero and place-number systems include the cited web pages and

We still use context in the interpretation of numbers in limited situations. For example, if you go to a store to buy candy and the clerk tells you the cost is two-fifty, you know he or she means $2.50. But if you are buying a dining room table at a furniture store and the clerk tells you that it costs two-fifty, you know that the dining room table costs $250.


Ask the class if they ever wondered why an hour has 60 minutes instead of 100. We inherited this from the Babylonian counting system used some 2500 years ago.


Many students have trouble with the concept of place value. You may want to have a student come to the board and change the place-values of several numbers, such as changing 2013 by replacing the number in the tens place with a 2 and in the thousands place to a 5 (creating, 5,023). You can then help the class write a large number using Roman Numerals, for example, 999 (CMXCIX), or an even larger number, 1,909,235 (MCMIXCCXXXV - the numbers in bold are to be written with a line above them that came to mean, in the late Roman Empire, that the number below the line should be multiplied by 1000). Point out how much more difficult it is to write numbers and perform numerical operations using Roman Numerals than the Arabic numbers we presently use.





















The Spaniards came from Europe and conquered Mexico and Central America. Over time they mixed with the indigenous Mayan population. When Mexico won its independence from Spain in 1821, its lands included California but it was very sparsely populated. U.S. settlers began to immigrate to California with the first wagon train reaching the state in 1841. California fell to U.S. troops in 1847 during the Mexican American War. Gold was discovered in 1848 and California became a state in 1850. Massive immigration of settlers from the U.S. overwhelmed the Latino population during the 19th century. Emigration from other parts of the United States continued through most of the 20th century. Increasing numbers of Mexican and Central American immigrants came to California during the 20th century, and if current demographic trends continue they will be a majority in a few decades. Many of Mr. Escalante's students were from Central America and had mixed Mayan and Spanish ancestry.




Use a large map of the world to show the locations of Greece and Rome and the flow of the ideas of zero and place holding from India, to the Middle East and from there to Europe. Also have a student show the population flows from Spain to Central America and from there to California. These resulted in Latinos becoming a growing minority in Southern California.



Sources for discussion of the origin of "the finger": Gestures: The DO's and TABOOS of Body Language Around the World, Revised and Expanded Edition by Roger E. Axtel, 1998, John Wiley & Sons, Inc., New York, pp. 43 - 49; Titanic Fingering; The Straight Dope; About.com article on Urban Legends and Folklore; Slate Magazine Article on "What Thumbs Up Means in Iraq"; The Finger, A Comprehensive Guide to Flipping Off;


We Can Get A Taste of Calculus in Finding the Area of a Circle

For this we go back to the ancient Greeks. Archimedes is the Greek mathematician who discovered the equation for the area of a circle. He did it by inscribing regular polygons in a circle. (A polygon is a figure with many sides. A square has four, a pentagon has five, a hexagon has six, and so on. In a regular polygon, all of the sides are equal.) All regular polygons can be divided into a number of right triangles. Archimedes knew the equation for the area of a triangle. He could therefore calculate the areas of regular polygons.

By increasing the number of sides of the polygon inscribed within a circle, Archimedes kept approaching closer and closer to the area of the circle. In other words, the area within the curve of the circle that was not in the polygon kept getting smaller and smaller. Archimedes found that the numbers he derived for the areas of the regular polygons as they got closer and closer to the curve of the circle approached the number π times the square of the radius of the circle (π r2).

π (pi) is a constant of nature. The numbers to the right of its decimal point never repeat and will keep going forever. They have no pattern that mathematicians have yet been able to discover. π, taken out to the ten thousandth is 3.1415.

Calculus permits mathematicians to determine the area under a curved line. It does this by finding the area of polygons with many sides that approach the shape of the curve. Calculus applies and extends the process discovered by Archimedes when he used regular polygons inscribed within the circle that approach the shape of the circle.

By using the same theory with three dimensional polygons, calculus permits mathematicians and engineers to determine the volume of spheres, cones, and other shapes. The importance of calculus can be seen in something as mundane as the calculation of the shape of a can of cola. Calculus is used to determine the shape and size which will most economically hold 16 ounces of soda. Companies can save millions of dollars each year through small reductions in the amount of aluminum used to make a can of soda.

Modern mathematicians believe that Sir Isaac Newton (an Englishman) and Gottfried Wilhelm Leibniz (a German) invented calculus independently and at about the same time. For many years there was a bitter dispute between their proponents over who invented calculus first. (In the movie, one of Mr. Escalante's female students tells her mother the story of the man who claimed to have invented calculus before Newton. She didn't have it quite right.)




This section can be used as a break toward the end of the movie or after the movie has ended. The following discussion should be accompanied by at least three diagrams of polygons inscribed within a circle demonstrating that the area of the circle outside the polygons diminishes as the number of sides of the polygon increases.





Sources include: Article on "Calculus" from Encyclopedia Britannica Premium Service, accessed 29 Feb. 2004 and The First Thousand Digits of Pi.


Literary Devices in a Work of Historical Fiction: Development of Character, Symbols, Subplots, Foils and Irony

Angel is a key character whose evolution exemplifies the transformation of the entire class. Angel sauntered into the class as a member of a gang: surly, insolent, and disengaged. The next scene involving Angel shows Mr. Escalante preventing Angel from helping his friends in a gang fight. Then, in class, Mr. Escalante taunted Angel and his friends with his "tough guys deep fry chicken" comments and Angel discovered that he understood the concept of zero. Then, although he was still frequently cold and hostile, Angel began to warm up by participating in the class. Angel's interest in staying in the class was shown when he bargained with Mr. Escalante for an extra book to keep at home. He didn't want his gang friends to see him taking books to and from class. In return for the extra book, Angel promised Mr. Escalante "production."

Angel is then shown caring for his grandmother and going out at night with his gang. He was late to class but charmed Mr. Escalante into giving him one more chance. But after spending the night at the emergency room with his grandmother, Angel was late again. This time Mr. Escalante wouldn't listen to any explanation and kicked Angel out of the class. By this time, Angel realized that success on the AP test could be a way out of the gang life. And so he came up with an innovative solution. He brought his grandmother to Mr. Escalante's house at Christmas to request that Angel be readmitted to the class. Mr. Escalante could not turn down an "abuela" at Christmas.

Angel was still a prickly fellow, as the fight with Pancho showed. He was still not completely comfortable with the class and did not trust them. Then, after the exam, Angel went swimming with his classmates. Angel was fastidious about his clothing and his image; the decision to put himself in a vulnerable position by taking off his clothes to swim with the class showed that he had finally bonded with them.

When the charges of cheating were made, Angel was deeply upset. Once more he went riding at night with his gang friend and taunted the police. But he realized he no longer fit in with the gang culture and walked away from a fight. He had enough faith in the system to retake the test. He passed with the highest possible mark, a five.

From the beginning of the film to the end, Angel's clothing is a tip-off to his growing relationship with the class and his diminishing relationship with the gang. At the beginning of the movie he was wearing a hair net. Through the course of the movie this disappeared and his clothing lost its gang identification, symbolizing his move from gang member to AP student. Note also that the clothing and general appearance of the other kids becomes increasingly neat and mainstream as the movie progresses.

Mr. Escalante is another fully developed character. We are shown his strengths as a dedicated teacher and his weaknesses, including his failure to pay enough attention to his family, his refusal to take care of himself, his refusal to listen to Angel's excuse, etc.

The plot in the film is relatively straightforward but there are also subplots. The primary subplot is the development and growth of Angel as a person, away from the gang culture and toward identification with the class. There are also little subplots relating to some of the students. There is the romance between two students and a subplot concerning the very bright girl whose family wants her to work as a waitress in the restaurant.

A "foil" is a relatively minor character in a play or film who acts differently than a major character in significant ways. Foils are used by authors and screenwriters to highlight, through contrast, important traits of the major character. In "Stand and Deliver," the foil for Mr. Escalante is the head of the math department who doubted that the students could learn calculus and thought that they had cheated. She had no faith in the abilities of the students. The foil for Angel is his gang friend. This boy was a gang banger when the movie started and had not changed by the end of the movie. He did not stay with the class and he did not take the AP Calculus exam. Without these two characters, the story wouldn't be nearly as rich and compelling as it is.

There is also irony in this story. Angel's name is ironic. He's not angelic at the beginning of the story. Even at the end when he bonds with the class and rejects his gang affiliations, he's no angel. The most important irony is that if the kids really cheated on Free Response Question #6 they got the wrong answer on the cheat but passed the test anyway. When the ETS caught on to the attempt to cheat, it made them take the test again. (The law of unintended consequences strikes again. (See discussion below.)



Suggestions for Using this Unit: The Introduction asks students to think about the literary devices used in this movie. It should be followed by a Comprehension Test on Literary Devices in a Work of Historical Fiction. In the alternative, the test can be used as a homework assignment.






BUILDING VOCABULARY: Ganas ("desire" in Spanish), "low expectations," "Advanced Placement Test," barrio, "overt racism," "covert racism."


Public Policy and Burdens of Proof in Modern Society (Perhaps the ETS Gave the Students a Break By Allowing Them to Take the Test a Second Time)

Jay Mathews was a journalist who specialized in writing about education. After the movie was released, he wrote a book about Jaime Escalante and his achievements as a teacher. Mr. Mathews was very sympathetic to Mr. Escalante and his students. He called his book Escalante: The Best Teacher in America. While he was interviewing people for the book, Mr. Mathews was asked by leaders of the East Los Angeles community to "put the [cheating] issue to rest and perhaps reveal once and for all how the ETS had erred in its investigation." The students agreed to answer his questions about the incident. The ETS provided a statement describing its investigation and justifying its actions. (Escalante: The Best Teacher in America 1988, Henry Holt and Company, New York, pages 143 - 179.)

Based primarily on Mr. Mathews' investigation, here are the facts that the ETS knew or could have discovered when it conducted its investigation in 1982:

1.   In order to test for cheating on the multiple choice section of the AP Calculus Test, ETS investigators used their computers to compare the answers of students from test sites all across the country. They found out how often any two students had the same or very similar answers. When they looked at the 18 Garfield High students who took the test, the ETS investigators found that 14 had levels of agreement in their answers that, nationwide, the ETS had found in only one out of every 100,000 pairs of test-takers. However, for the Garfield High students it happened with 14 students out of the 18 who took the test. Reducing the fraction (14 out of 18 = 7 out of 9) that means that 7 out of every 9 Garfield High test-takers had the same degree of agreement in their answers as the ETS had found in only 1 out of 100,000 students across the country. That is a big difference. There are only two possible explanations. One is that the Garfield High students cheated on the multiple choice section of the test. The other is that there was some other reason that applied only to the Garfield High students that caused their answers on the multiple choice section of the test to be the same or very similar. (Mathews pg. 157.)

2.   The students at Garfield High who took the test scored well above the national average. They averaged four mistakes each, while the national average was 18.

3.   Mr. Escalante drilled and re-drilled his students in a systematic approach to calculus. He expected a high degree of agreement in the answers they gave.

4.   The proctor who supervised the examination saw no suspicious behavior and no evidence of cheating. She reports that she was out of the room only for a very short period of time during the test.

5.   The 18 students were together in a room and if 12 of them were copying, one of the students who didn't participate would have been likely to report them.

6.  The seven word problems were called "Free Response Questions" (FRQs). Students could get a passing score of "3" on the exam with correct answers to only three of the seven FRQs or with partially correct answers to six of the seven questions. FRQ #6 is set out below. You don't have to understand calculus to see how the answers by the twelve students caused grave concern to the ETS.
#6: A tank with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 4 meters and its volume is 36 meters. If building the tank costs $10 per square meter for the base and $5 per square meter for the sides, what is the cost of the least expensive tank? (Mathews pg. 144.)
The twelve students began with an identical incorrect formula for the cost of the rectangular tank. Each of them also made an identical mathematical error while simplifying a fraction. Students are taught how to simplify fractions in the 6th or 7th grade. In order to do the work in their math classes they must perform the operation hundreds, if not thousands, of times. In other words, these twelve students were masters at simplifying fractions. In FRQ #6 they had to substitute 9/w for h in the term 10hw. The answer is 90.
If h = 9/w then

10hw = 10 X 9 X w = 10 X 9 X w    =    90
                   w                    w


The two w's cancel each other out and the expression simplifies to 90.
The twelve students made an identical error in this simple computation. From the examinations that he saw, Mr. Mathews confirmed the ETS' claim that students who started with the incorrect formula also made an identical mistake simplifying the fraction. (Mathews pg. 175.)

7.   As Mr. Escalante stated in the movie, it could have been that the teacher made the error and taught the students the incorrect formula. The class had been taught by a substitute teacher during Mr. Escalante's illness. This problem was covered at that time. (However, six of Mr. Escalante's students got the correct answer or didn't make the same errors as the twelve students. Moreover, this explanation does not account for the identical error in reducing the fraction.)

There is also information relating to the issue of cheating that was not known to the ETS in 1982. (Teachers may want to wait and disclose this to their classes after the discussion of the evidence available to the ETS.) Mr. Mathews interviewed some of the students under a promise of anonymity. The first two students he spoke with admitted that another unnamed student was trying to be helpful and had passed around a piece of paper with what later turned out to be the incorrect answer to FRQ #6! Later most of the students, including one of the students who had admitted that there was cheating, signed a joint letter to Mr. Mathews saying that there had been no cheating. The other student who had told Mr. Mathews about the piece of paper that was passed around wrote to him separately stating that he had been "joking" to test a theory that the journalist was an agent of the ETS. The student wrote: "I told you lies. Nothing but lies." At that point Mr. Mathews abandoned his investigation without coming to any final conclusion. (Mathews, pg. 177.)

SUGGESTIONS FOR PRESENTING THIS UNIT: The motivating factor in this unit is the evidence that twelve of the students cheated. The complexity of the classroom presentation will depend on the abilities of the students to whom it is taught and the time available. Younger or below average students in situations with little time may be able to absorb only an explanation of "Lady Justice," her blindfold and scales, and the burdens of proof in civil and criminal cases. Older or more capable students in situations in which there is more than one class hour to devote to this discussion can be introduced to the role played by public policy and burdens of proof in civil, criminal, and non-governmental proceedings.

TWM suggests the following sequence for this unit. It assumes that the points 1 - 4 and 8 have been made in the Introductory Lecture and that the students have seen the movie. First, teachers can assign as homework, for the days when the film is shown, the handout on Public Policy and Burdens of Proof. (This is based on U.S. law.) As with all TeachWithMovies.com materials, teachers should feel free to edit the handouts to suit the needs of their classes. Students should be required to read the handout.

Then hold a class discussion. The first topic is to review and confirm the lessons of the handout by asking students which public policies determine how the law should come out on various issues: Examples are: 1) Self-defense as an excuse for killing someone; 2) the death penalty; 3) a three strikes law; 4) a zero tolerance policy for cheaters in school.

Second, sitting as the "board of directors" of the ETS, the class should debate and select a burden of proof to use in determining if the 12 students cheated. See Burdens of Proof Chart and Burden of Proof Instructions. Teachers should make sure that the "board" (the class) is mindful of its responsibility to take reasonable care to avoid injuring the students who take its tests: both the students accused of cheating and the students who aren't accused of cheating. The possible adverse publicity if it appeared to be discriminating against Latino students would also concern "board" members.

Third, based on Facts that the ETS Knew or Could Have Discovered in 1982 the class debates and then votes on whether the evidence known to the ETS in 1982 met that burden.

Fourth, based on its conclusion, the class should evaluate the response of the ETS when it invalidated the first test scores and allowed the students to take the test a second time. Was there a better way to handle the situation?

The most important points to get across in the discussion are that the major public policy in our society is freedom of action. Individuals and organizations like the ETS should be allowed to do what they think is best. However, because we live in society with other people, very often our freedom of action is limited by an important intervening value. In this case, the value that limits the application of the general public policy is that every person and every organization needs to take reasonable care that its actions do not injure others. Applied specifically to this situation, the ETS should be required to take reasonable steps to avoid injuring the students when it grades their tests scores and makes a determination of whether or not the students cheated, while at the same time upholding the integrity of its tests.

Assuming that the "board" determines that the students cheated, in evaluating its own response, the following points should be raised and the class should decide if they are legitimate concerns:

  1. These students had worked hard and knew the materials as shown by the fact that they passed the test without any credit on FRQ #6; such an effort normally merits a substantial reward; this is especially true because the students came from a poor, culturally deprived families; they had more to overcome than kids from middle or upper class backgrounds;
  2. Cheaters ordinarily don't get second chances; giving stiff penalties to cheaters is generally a good way to deter cheating;
  3. The students didn't have a history of cheating;
  4. The students were under special pressures to pass the test; the pressure came from their school, from Mr. Escalante, and from their situation as Latino children from a poor neighborhood trying to show the world that they could master calculus;
  5. Having to retake the test was itself a substantial penalty which required the students to study all summer to keep their skills up;
  6. The Garfield High School math program was on the verge of shattering a pernicious myth that kept students from achieving their full potential; disqualifying the test scores of such a large number of students for cheating would have grievously hurt the program; there would be benefits to tens of thousands of children yet to take calculus in permitting the students to take the test a second time when it appeared that they would pass it.

There are several other ways to present this information. The discussion of public policy and its influence on choices about the burden of proof can be presented by lecture or class discussion confirming what is in the handout. (Teachers can use the Burdens of Proof Chart and the Burden of Proof Instructions as visuals to help present the lecture.) The teacher can select a burden of proof or the class can select one, sitting as the board of directors of the ETS. The teacher can then, through a mixture of class discussion and lecture or simply straight lecture, present the students with the information available to the ETS in 1982 on the question of whether the students cheated. See Facts that the ETS Knew or Could Have Discovered in 1982.

Another alternative is for teachers to assign students to teams to advocate one burden of proof or the other to the "board of directors" and to serve as prosecution or defense attorneys in a "board" proceeding to determine if the students cheated. Students not assigned to teams will act as "board" members to vote on the various issues. For example, three teams can present arguments for the most likely burdens of proof: (1) Beyond a reasonable doubt; (2) clear and convincing evidence; (3) preponderance of the evidence. Each team will be given the Burdens of Proof Chart. They will be instructed to deal with each of the arguments and questions that it describes. They should also have the Burden of Proof Instructions available if they need it. Each team of students should be encouraged to come up with other public policy arguments supporting their position. Each should choose a person to give a short presentation supporting their position to the class. The "board of directors" will then discuss the points made and vote on the burden to be applied. The teacher or an elected student will moderate the discussion as the "chairman of the board." Then the other two teams, one as ETS prosecutor making the case that the students cheated and the other defending the students, will present their cases. The teacher should sit as the moderator, select and impose a time limit for arguments and deliberations, and give an instruction as to the terms of the standard being applied. See Burdens of Proof Instructions. The time allowed for argument can be divided between main argument and rebuttal. The class then deliberates as the "board of directors" to make its decision about what to do in the situation.

After the vote, the students can be assigned an essay to be written in class or as homework stating their vote on both issues and presenting their reasons. Or, they can be given the comprehension test/homework on burdens of proof. An answer key can be found at Stand and Deliver - Answers to Comprehension Tests and Discussion Questions.

There are also a number of other interesting class discussions that can be held based on this film and Mr. Mathews' revelations. After the discussion has been completed and the "board" has voted, the teacher should tell the class that cheaters ordinarily don't get second chances to take the test even when they know the material and would pass a retest. Ask the class whether the students should have been given a second chance or whether this was a case of reverse discrimination in which students were treated more leniently because they were members of a minority. There is no one correct answer to this question but we tend to think that the ETS reached the right result.

At this point, teachers can tell the class about the admissions by two students that there was cheating and their subsequent retraction of those admissions.

Then ask whether, assuming that the 12 students did cheat on FRQ # 6, the message of the movie was seriously undercut. This question has an answer, and it is "no." Clearly these students knew calculus. The ETS put them under special scrutiny in the second exam and they still passed. The facts found by Mr. Mathews have an impact on how we see the events of the film and they teach their own lessons about cheating, but the core messages of the film are that inspired students can achieve wonders and that something very good for math education, for the Latino community, and the nation as a whole happened at Garfield High. The evidence indicating that students who knew the material and could pass the exam, under extreme pressure, cheated on one question does not negate their achievement in mastering calculus.

Another interesting discussion can explore the law of unintended consequences. Define it for the students: "Whether or not what you do has the effect you intend, it will have consequences that you don't expect." Note, if you have not done so already, that the movie departs from fact when it says that the students had one day to study for the second test. In reality, the second test wasn't given until August and the real students had to spend the summer after their senior year studying long hours with Mr. Escalante. Ask students how the law of unintended consequence applied to this situation. (When the students cheated, they had no idea that it would mean that they would have to study all summer and take the test again.)

Teachers can also use this situation to illustrate the concept of irony. First, these students didn't need to cheat. They passed the exam the first time without any credit on FRQ #6 and then they passed a different AP Calculus test about three months later. Second, in their effort to cheat, they got the wrong information. In other words, the cheating didn't help the students get their passing grades the first time around and they suffered a substantial penalty by having to take the test again. This is an example of
situational irony.

The lecture and exercise described in this section will lead students to: (1) think critically about the presumption of innocence and the different burdens of proof used by various institutions in society; (2) logically evaluate a set of facts; and (3) look objectively at the assumptions of a very compelling movie.



Materials Provided for this Unit: (1) Student Handout Public Policy and Burdens of Proof (to be given to the class before showing the movie or after it has started), (2) Student Handout What the ETS Knew or Should Have Known (to be handed out during class discussion after movie has been shown); (3) Burden of Proof Jury Instructions; (4) Which Burden of Proof Should the ETS Be Held to in Determining if the Students Cheated?; (5) Comprehension Test on Public Policy and Burdens of Proof: Perhaps the ETS Gave the Students a Break and (6) an Answer Key to the tests and discussion questions.

Items 1 - 6 are presented in a format suitable to be printed and distributed to a class. It can also be modified by the teacher for the needs of the class. The test can be used as a homework assignment.












Statue of Lady Justice


The evidence for the plaintiff (the government in criminal cases) is placed on one side of the scale. The evidence for the defendant is placed on the other side of the scale. In a criminal case, the scales must tip very far down on the prosecution's side (beyond a reasonable doubt) before the accused can be convicted. The burden of proof in a civil case is a preponderance of the evidence (the plaintiff must prove that its claim is more likely true than not true). In civil cases the scales need tip toward the plaintiff only by the slightest amount for the plaintiff to win. If the scales are even or if they tip away from the plaintiff, the defendant wins.




In the discussion, ask the class if they have any questions about the written materials and use that as an opportunity to explain the points made in the handout. Feel free to give examples of how the burdens of proof work in the real world. (One example is from the O.J. Simpson case. The government was not able to produce enough evidence to satisfy the jury in the criminal case "beyond a reasonable doubt" that Mr. Simpson had killed his wife and Mr. Goldman. However, when the families of Goldman and Mrs. Simpson brought a civil suit for damages for wrongful death against Mr. Simpson, they were able to convince a second jury that it was more likely true than not true (a "preponderance of the evidence") that Simpson had done the killing. So, Mr. Simpson goes free but the families have a large judgment for money damages against him.)





Often, as in the O.J. Simpson case, one action violates both criminal and civil standards of care. Another example is a building owner who allows a dangerous condition to remain on his or her property. The owner may be liable for criminal penalties for building code violations if the state can prove the existence of the violations "beyond a reasonable doubt." If someone is injured in the building as a result of the conditions, that person can bring a civil suit for damages. The plaintiff only needs to establish the building code violations by "a preponderance of the evidence" (more likely true than not true) in order to recover for his or her injuries. People who drive their cars while drunk are in the same situation. They can be imprisoned for drunk driving and if they injure someone, the injured person can recover damages in a civil suit.



Click here for Social Studies curriculum standards for the eleven most populous states relating to the issues raised by this movie.








At some point in the discussion the teacher should note that Mr. Mathews' study was not made until after the film had been released.


















The ETS was also concerned with its image with the public. The students and their supporters claimed that the ETS was discriminating against the students. Thus, the ETS was interested in fashioning a result that satisfied the students and their supporters while upholding the standards of its tests. Public disclosure or the threat of it has an important role in making sure that large institutions are sensitive to the needs of ordinary people.









During class discussions about the evidence for and against Mr. Escalante's students look for reasons that should not be considered such as considerations based on race, ethnic origin, friendly feelings, etc. Comment that these will not be considered by justice which is "blind" to considerations based on class, race, sex, etc. An example: "The ETS was justified in being suspicious of a large group of Latino students from one school who did very well on the AP Calculus test because it knew from experience that, in the past, Latino students hadn't done well in math."





Note: Why does Lady Justice have a blindfold over her eyes? It's not because she doesn't see the truth. Instead it means that she does not take into account the race of the parties in dispute, their national origin, whether they are celebrities, and other factors that do not bear on the truth of the disputes to be decided. She simply weighs the evidence in her scales.



A note on the presumption of innocence. It only relates to criminal cases. However, belief in the rightness of this presumption is so strong in our society that most people think reason requires that the presumption of innocence be extended to cover decisions by government agencies, individuals, and non-governmental organizations that have important effects on the lives of individuals. While there is no accepted name for the presumption of innocence when applied to non-criminal situations, it can be described as the "presumption of good conduct." Thus, the vast majority of people believe that someone should not be found to have done something wrong unless there is some evidence supporting that conclusion.

How do presumptions work? They are not independent evidence to be put into the determination of guilt or innocence. (They have no weight in the scales of "Lady Justice.") In criminal cases the effect of the presumption is only to place upon the state the burden of proving the defendant guilty beyond a reasonable doubt. (E.g., California Penal Code Section 1069.) The same is true of the presumption of good conduct in a jury case. It means that at the beginning of the trial the jury assumes that the defendant acted properly. However, once the plaintiff presents any credible evidence to the contrary, the jury can find liability without reference to the presumption. In a criminal case, once the state provides evidence, the jury assesses whether there is a reasonable doubt without reference to the presumption of innocence.





On the state or national level, public policy applied to circumstances leads to (1) laws, regulations, rules of conduct for individuals and organizations and (2) public programs such as Social Security, Medicaid, construction of roads and bridges, schools, etc.


On the personal level, values (what we cherish) applied to circumstances lead to (1) principles of conduct and (2) action.




Some Problems With Cheating

Cheating is unethical. -- Ethics is the study of how to align ourselves with what is right and good in the universe. One of the basic needs of all mankind is a sense of belonging. The most important thing to belong to is the positive force of the universe. (The word "integrity" comes from the word "integer" which means "whole.") Many people call the universal positive force God; others call it something else. But whatever they call it, all people have their own personal definition of what is holy. Conduct that we know is dishonest separates and isolates us from the greater good in the universe.

The reasons people give for cheating are to get better grades, to avoid studying, and to get an advantage over others. These all pale in comparison to the isolation and separation that are the result of dishonesty.

This concept may be difficult for many students. First, it takes experience and maturity to realize the advantages of feeling united with the good forces of the universe. Second, many people don't mind living separate and isolated for years, or even decades, while they focus on accumulating wealth, advancing in their careers, partying, etc. Third, many adolescents derive a sense of belonging from their peer group which can, at times, lead them to do things they would otherwise consider to be unethical.

Students should be encouraged to look at the future. If people don't believe they are acting in concert with the good, all of their relationships are based on quicksand. Acting unethically leaves us isolated. Explained in this way, ethics is not some far-off standard set by religious leaders and parents. It is intensely personal and vital; affecting ultimate issues of union and separation.

A second reason not to cheat is that dishonesty isolates us from our true friends and loved ones. -- The question here is, "Would you want to be the friend or family member of a person who cheated when things got difficult?" Friends and family need to be able to believe what we tell them. They need us to be responsible, that is, to do what we should do. They need us to be fair and not to take advantage of others. And they'd like us to be caring. Cheating fails to meet three of these requirements:
Cheaters aren't trustworthy; their cheating involves lying.

Cheaters aren't responsible; they're doing something they know they shouldn't and they're letting other people down. (The obligation of students is to learn the materials and then take the tests. Cheaters aren't doing that. If Mr. Escalante's students cheated, other than themselves, it was Mr. Escalante who they let down the most. Mr. Escalante had made many sacrifices for them and worked very hard to prepare them for the test. The students put all that work in jeopardy by cheating.)

Cheaters aren't acting fairly; they are trying to profit from a secret, dishonest advantage over students who don't cheat.
Third, cheating in education is self-destructive. -- Often, tests are learning experiences in themselves. When we take a test, the information or problems in the test are added to our own knowledge base. In addition, most knowledge builds on what was learned before. This is especially true in mathematics. If we cheat and don't learn the topic fully, then we'll be at a disadvantage in the next level of difficulty. For example, the purpose of the AP Calculus test is to determine if students know enough to skip the first year of calculus at the college level. If students enter the second year of college level calculus when they haven't mastered the first year, they'll have a much more difficult time than students who learned first year calculus thoroughly. This applies to just about any other subject such as science, history, English, and foreign languages. Students will be asked to perform skills at progressively higher levels as they advance through their schooling. For example, essays that are acceptable in the seventh grade will receive a failing mark in the 12th. Students will be expected to draw on a broader knowledge of facts as they get older. History teachers often ask students to draw comparisons between one epoch and another, or between one country and another. English and literature teachers may ask students to analyze a story for symbols and then several months or grade levels later ask that this be done again but with more sophistication and complexity.

Fourth, cheating is destructive to our own self-image. -- Would you like to view yourself as someone who gets ahead only because they cheat and take shortcuts? What does it do to someone's self-image to know that the only way that they can compete with other people or deal with a teacher is through dishonesty and by getting an unfair advantage?

The fifth reason not to cheat is that you might get caught. -- Assuming that Mr. Escalante's students did cheat on Free Response Question #6, they discovered some of the penalties for getting caught. The ETS wanted to invalidate their test scores. Their great triumph had become a disaster. The students were lucky to be allowed to take the test again; this time under close supervision by ETS personnel. At the very best, the students had to study for another summer and take the test a second time. Not a pleasant prospect. But these kids were fortunate. Often when a school or testing service believes that students have cheated, they are given no second chances.

Finally, when cheating involves adopting someone else's answer rather than your own, you are actually demeaning yourself. -- You are saying that what you have to say is wrong or not important and that what they have to say is right and more important. This doesn't apply so much to courses like math or science, but in English or history or any of the arts it is important. In all of those subjects your interpretation and your insights are what is important.

Comprehension Tests

COMPREHENSION TEST ON THE MOVEMENT OF IDEAS AND A TASTE OF CALCULUS

1.   What is the great advantage of place-value numbers?

2.   Describe in your own words the concept of place-value numbers. After giving your description, demonstrate it by describing what the numerals 5 and 8 mean in the number 545,680.

3.   Why was it so hard for people to come up with the concept of nothing as a number? When did the concept of the zero come to Europe?

4.   Name the first two civilizations that used both the concept of zero as a number in computation and place-value numbers. Give the approximate dates of the development.

5.   Name two advanced civilizations in Europe that flourished after the concept of place-value numbers was created in Babylon but which did not know this concept.

6.   Describe the movement of the concept of zero and place-value numbers to the Americas after the Mayan civilization declined.

7.   Name four advanced characteristics of culture developed by the Maya.

8.   Trace the movement of the insult of giving someone "the finger" from the earliest evidence that it was used to 20th century United States.

9.   Explain how Archimedes, the ancient Greek mathematician, found the area of a circle and how that relates to calculus. Draw diagrams if it would help in your explanation. (The answer to this question counts for two points.)

This Learning Guide presents two tests in addition to the test immediately to the left. They are:



This test assumes that students have been given the information in the Helpful Background sections entitled Examples of the Movement of Ideas: Zero and "the Finger" and Finding the area of a Circle: A Taste of Calculus.



For an answer key to this test, click here.






For a printable version of this test suitable to be distributed to a class, click here


COMPREHENSION TEST ON LITERARY DEVICES IN A WORK OF HISTORICAL FICTION

1.   Compare the way the characters were at the beginning of the movie to the way they were at the end. Which character changed the most?

2.   Angel is an interesting character, constantly getting into trouble and constantly figuring a way to get out of it. What drove this character?

3.   At the beginning of the movie, Angel is wearing a hair net. What did that mean?

4.   Remember the scene in which Mr. Escalante pinned Angel against a fence and stopped him from joining a gang fight? That action by Mr. Escalante had several meanings for Angel. Name one of them.

5.   By the time Angel brought his grandmother to Mr. Escalante's house at Christmas, how had his character changed?

6.   Just before the class went swimming in the ocean to celebrate the exam being over, what was Angel's clothing like?

7.   It was difficult for Angel to decide to join the class when they went swimming to celebrate finishing the exam. The scene begins with Angel fully clothed standing on the shore and the rest of the class in the water. What was the significance of Angel taking off his clothes and jumping into the water to be with his classmates?

8.   After the first examination results had been invalidated and Angel had provoked the police, his gang friend challenged him to a fight. Why did Angel walk away from that fight and what did this symbolize?

9.   In this movie there is one character who is a foil for Mr. Escalante and another who is a foil for Angel. Who are these characters and which of their traits make them foils for Mr. Escalante and for Angel?

10.   The movie opens with a long shot of the Los Angeles River, which is a concrete ditch for much of its length. What is the symbolism of this shot? How does it relate to the rest of the film?






This test assumes that students have been given the information in the section entitled Literary Devices in a Work of Historical Fiction





For a printable version of this test suitable to be distributed to a class, click here





For an answer key to this test,    click here.


COMPREHENSION TEST ON PUBLIC POLICY AND THE BURDEN OF PROOF (PERHAPS THE ETS GAVE THE STUDENTS A BREAK BY ALLOWING THEM TO TAKE THE TEST A SECOND TIME)

1.   What is a good description for the presumption of innocence when applied to civil cases or private matters? Here is a hint: the term was discussed in the lecture and it has five words. Then describe why we don't just use the term "the presumption of innocence" for civil cases and private matters.

2.   The chart below mixes up the burdens of proof (on the right) with some of the different situations in which decisions are made in our society (on the left). Match the type of proceeding with the letter assigned to the burden of proof.

Criminal prosecution                A.   preponderance of the evidence
Civil lawsuit for damages                B.   no accepted burden
of proof but the action
must be reasonable
in the circumstances
in light of the common
law obligation to take
reasonable care to
avoid injuring people
Decision or action by a
person, a business,
or a non-governmental organization               
C.   beyond a reasonable doubt


3.   The determination of the proper burden of proof in different situations depends upon the facts of the situation and considerations of public policy. Briefly describe some of the public policy considerations supporting the general burdens of proof for: (1) criminal prosecutions; (2) civil law suits; and (3) private, non-governmental determinations. There are some exceptions and extraordinary situations in which the burdens of proof are modified. In your answer, don't worry about the exceptions and extraordinary situations, just refer to the general rules.

4.   What burden of proof do you think the ETS should have used in making a determination of whether or not the students cheated? Give your own opinion among the burdens of proof we have discussed in class and briefly describe why you came to that conclusion. Set out the public policies that support your contention. (The answer to this question counts for two points.)

5.   Apply the burden of proof that you selected in response to the preceding question to the facts known to the ETS when it disqualified the test scores and offered to have the students take the test again. Use the facts found by Mr. Mathews in his investigation. Discuss: (1) whether the burden of proof was sustained with respect to the suspicions of cheating based on the unusual rate of similar answers to the multiple choice questions and (2) whether the burden of proof was sustained with respect to the suspicions of cheating in answering Free Response Question #6.

6.   Do you think that these students deserve a chance to take the test a second time?

7.   If a group of middle class students took an AP Calculus test and passed but cheated on a question that they got the wrong answer to, should they be permitted to take the test a second time? Assume that the students had no history of cheating.

8.   Does the information that Mr. Mathews developed about whether or not the students cheated on Free Response Question #6 undercut the core message of the film?









This test assumes that students have been given the information in the section entitled Public Policies and Burdens of Proof: Perhaps the ETS Gave the Students a Break



Students will need to have available for question # 5 the handout entitled Facts that the ETS Knew or Could Have Discovered in 1982.



For a printable version of this test suitable to be distributed to a class, click here



For an answer key to this test,    click here.



Where does this go?



FOR SUGGESTED ANSWERS:   click here.



Additional Assignments


Continued from the Learning Guide...

See additional Assignments for use with any Film that is a Work of Fiction. Question: Regardless of the facts presented in the film, what do you think would motivate students to cheat on a test for which they are clearly prepared?Suggested Response: Answers will vary. Lack of confidence is a major factor in the urge or decision to cheat on any test. Fear of failure may also serve as a motivation.

Social-Emotional Learning Discussion Questions


MALE ROLE MODEL

1.   Do you think that Mr. Escalante is a role model for a teacher?

2.   The film shows some of Mr. Escalante's mistakes. Can you describe three of them?

SELF-ESTEEM

3.   Would you be willing to give up your mornings, afternoons, and weekends, and a good part of your summer to prove to yourself that you could learn calculus and pass the AP Calculus test?

4.   Describe the corrosive effects of the loss of self-esteem to the students in this film before they met Mr. Escalante.

EDUCATION

5.   One of Mr. Escalante's special qualities was that he had high expectations for his students. What is the importance of a teacher's expectations for a class?

6.   Did Mr. Escalante do the right thing in going to the restaurant owned by the family of one of his female students to persuade the girl's father to allow her to attend the extra calculus classes? What is the appropriate role for a teacher when communicating with a student's family?

7.   Describe some of the techniques that Mr. Escalante used to keep his students interested in the class.

8.   Remember the lady who was head of the math department at Garfield High School? This teacher had low expectations for her students and thought that Mr. Escalante's students had cheated. What caused her to have these attitudes?

9.   What does this film tell you about the special contributions that inspiring teachers can make to their students and their community?

TRUSTWORTHINESS

(Be honest; Don't deceive, cheat or steal; Be reliable -- do what you say you'll do; Have the courage to do the right thing; Build a good reputation; Be loyal -- stand by your family, friends and country)


1.   The ETS was faced with strong evidence that the students had cheated. This came from their incorrect responses to Free Response Question #6, in which most of the class applied the same incorrect formula to the problem and made an identical mistake in simplifying a fraction, a type of calculation that they had been doing correctly since the 6th or 7th grade. Assume that the students cheated on Free Response Question #6. Discuss the role of the law of unintended consequences in the outcome of this situation.

2.   Assume that the students cheated on Free Response Question #6. Describe three reasons why cheating at school is not a good idea and how this relates to the situation of the students in Mr. Escalante's class.

RESPONSIBILITY

(Do what you are supposed to do; Persevere: keep on trying!; Always do your best; Use self-control; Be self-disciplined; Think before you act -- consider the consequences; Be accountable for your choices)


3.   Many teachers and school administrators, as well as children and parents have seen this film. Why aren't all children taking the AP Calculus test or engaging in some other specialized effort to excel? What about you? Are you making some special effort in your life to excel?

4.   Mr. Escalante got angry at Angel and unfairly punished him. The only reason that this did not have disastrous consequences was that Angel was committed and resourceful. How does this incident show the need for self-control by both Angel and Mr. Escalante?


Moral-Ethical Emphasis Discussion Questions (Character Counts)
(TeachWithMovies.com is a Character Counts "Six Pillars Partner"
and  uses The Six Pillars of Character to to organize ethical principles.)

Discussion Questions Relating to Ethical Issues will facilitate the use of this film to teach ethical principles and critical viewing. Additional questions are set out below.



Bridges to Reading:

Books that can be read in conjunction with this film are biographies of people from disadvantaged backgrounds who nonetheless excelled in their work. Examples are: Sal Si Puedes by Victor Chavez, Yes I Can by Sammy Davis, Jr. and Go Up for the Glory by Bill Russell. Jaime Escalante: Sensational Teacher by Ann Byers, 1996, Enslow Publishers, Inc., Springfield, N.J. was written for students grades 6 - 9. Escalante: The Best Teacher in America by Jay Mathews, 1988, Henry Holt and Company, New York, is a full scale biography of Mr. Escalante. Another wonderful book is The Story of My Life by Helen Keller (1902).

Links to the Internet:

For a more complete description of what happened to the Garfield High School calculus program, see Reason OnLine -- The untold story behind the famous rise -- and shameful fall -- of Jaime Escalante, America's master math teacher. A partial rebuttal to this article is contained in Science Insights from the National Association of Scholars.


Selected Awards, Cast and Director:


Selected Awards:   1989 Independent Spirit Awards: Best Actor (Olmos); Best Director (Menendez); 1988 Academy Awards Nominations: Best Actor (Olmos); 1989 Golden Globe Awards Nominations: Best Actor (Olmos); Best Supporting Actor (Lou Diamond Phillips).

Featured Actors:   Edward James Olmos, Lou Diamond Phillips, Rosanna De Soto, Andy Garcia, Will Gotay, Ingrid Oliu, Virginia Paris, Mark Eliot.

Director:   Ramon Menendez.

Additional Discussion Questions:

Continued from the Learning Guide...



QUICK DISCUSSION QUESTION:  One of Mr. Escalante's special qualities was that he had high expectations for his students. (1) What is the importance of a teacher's expectations for his or her students? (2) How do parents' expectations affect the performance of children in school? (3) What role is played by a person's own expectations?

Suggested Response: (1) and (2): If the adults around a child do not have high expectations it will be difficult for the child to have high expectations. (3): But the most important expectations are those that people develop and confirm on their own. [After students answer this question, parents and teachers can note that Anne Frank in her diary entry for July 15, 1944, just a few days before the Nazis found her family's hiding place, said this: "I understand more and more how true Daddy's words were when he said, 'All children must look after their own upbringing.' Parents can only give good advice or put them on right paths, but the final forming of a person's character lies in their own hands." Anne Frank died in the concentration camps.]

Many of the questions in the Comprehension Tests are also excellent discussion questions.

1.   See Discussion Questions for Use With any Film that is a Work of Fiction.

2.   How does the concept of "ganas" apply to this film? Can you achieve great things without it? Suggested Response: "Ganas" means "desire" or "longing", as in the desire to win. One cannot achieve great things without "ganas".

3.   Do you have "ganas" about anything in your life? Suggested Response: There is no one right answer to this question. A good answer will be heartfelt and meaningful.

4.   What steps did Mr. Escalante and Mr. Gradillas (the principal at Garfield) take to improve the math knowledge of the students who were coming into the calculus class? Suggested Response: The success of Mr. Escalante's class on the 1982 AP Calculus test was the culmination of a six year effort by Mr. Escalante. To help students acquire the background in geometry, algebra II, math analysis, and trigonometry necessary to understand calculus, Mr. Escalante encouraged area junior high schools to offer algebra in their eighth and ninth grade mathematics classes. He also convinced them to upgrade the standard of instruction. Escalante, supported by his principal, Peter Gradillas, also worked to impose higher standards in the pre-calculus math classes offered at Garfield. Mr. Escalante also taught intensive math classes during the summer.

5.   Why isn't the calculus program set up by Mr. Escalante in operation today? Suggested Response: Mr. Gradillas, the principal, went back to school to get his Ph.D. The new principal at Garfield High didn't support the AP Calculus program. Faculty members at the school were upset that so many resources were being devoted to the calculus program. Mr. Escalante left the school when the program would no longer be supported.



ANSWERS TO SOCIAL-EMOTIONAL LEARNING DISCUSSION QUESTIONS

MALE ROLE MODEL

1.   Do you think that Mr. Escalante is a role model for a teacher? Suggested Response: Yes. He cared about his students. He was innovative. He held his students to high standards. He knew how to motivate his students. He knew his subject matter. He had a goal which was difficult and he was helpful to other people. He worked hard to accomplish that goal.

2.   The film shows some of Mr. Escalante's mistakes. Can you describe three of them? Suggested Response: They include the following: (1) not listening to Angel's excuse when Angel was late because he was at the emergency room all night with his grandmother; (2) making fun of the personal life of one of the girls in the class; (3) getting angry at the ETS employees and thinking that they were discriminating against his students; (4) threatening one of the ETS investigators; (5) leaving the hospital when the doctors told him that he was not well enough to leave; and (6) not spending enough time with his family.

SELF-ESTEEM

3.   Would you be willing to give up your mornings, afternoons, and weekends, and a good part of your summer to prove to yourself that you could learn calculus and pass the AP Calculus test? Suggested Response: There is no one right answer to this question. Just asking the question is helpful because it stresses how difficult it was for the students to follow Mr. Escalante's program.

4.   Describe the corrosive effects of the loss of self-esteem to the students in this film before they met Mr. Escalante. Suggested Response: There is no one right answer to the question. The basic problem is that low self-esteem prevents people from achieving their full potential and taking the steps necessary for their own happiness.

EDUCATION

5.   One of Mr. Escalante's special qualities was that he had high expectations for his students. What is the importance of a teacher's expectations for a class? Suggested Response: Without high expectations from the teacher, few students in the class will work up to their full potential.

6.   Did Mr. Escalante do the right thing in going to the restaurant owned by the family of one of his female students to persuade the girl's father to allow her to attend the extra calculus classes? What is the appropriate role for a teacher when communicating with a student's family? Suggested Response: Mr. Escalante did the right thing. It is legitimate and helpful for teachers to point out to parents a child's special gifts or an unusual opportunity for the child at school. [Then have a discussion based on the following questions, "Would your answer be the same if the teacher had not been Latino but instead Anglo or Asian?" The answer, of course, is yes.]

7.   Describe some of the techniques that Mr. Escalante used to keep his students interested in the class. Suggested Response: The response should show that the students paid attention to the film. They include: the barbecue, the funny language, putting a student on a stool in front of the class for not doing her work, clowning around, making jokes, etc.

8.   Remember the lady who was head of the math department at Garfield High School? This teacher had low expectations for her students and thought that Mr. Escalante's students had cheated. What caused her to have these attitudes? Suggested Response: There is no one right answer. A good answer will refer to the fact that she was basing her conclusions on her experience. She was beaten down by the lack of resources, by the difficult students, and her inability to inspire her students. In this she was not alone. Many other teachers at Garfield High and at schools like it all over the country have suffered similar experiences and many have reactions that are similar to hers.

9.   What does this film tell you about the special contributions that inspiring teachers can make to their students and their community? Suggested Response: They can make an important contribution.

ANSWERS TO MORAL-ETHICAL EMPHASIS DISCUSSION QUESTIONS (CHARACTER COUNTS)

Discussion Questions Relating to Ethical Issues will facilitate the use of this film to teach ethical principles and critical viewing. Additional questions are set out below.

TRUSTWORTHINESS

(Be honest; Don't deceive, cheat or steal; Be reliable -- do what you say you'll do; Have the courage to do the right thing; Build a good reputation; Be loyal -- stand by your family, friends and country)


1.   The ETS was faced with strong evidence that the students had cheated. This came from their incorrect responses to Free Response Question #6, in which most of the class applied the same incorrect formula to the problem and made an identical mistake in simplifying a fraction, a type of calculation that they had been doing correctly since the 6th or 7th grade. Assume that the students cheated on Free Response Question #6. Discuss the role of the law of unintended consequences in the outcome of this situation. Suggested Response: They passed the test without getting the benefit of their cheat because they gave an incorrect answer to the question on which they cheated. This meant that if the ETS had not allowed them to take the test again, they would have been denied the goal that they had worked so hard to achieve. They would also have been branded as cheaters. In this case, ironically, the cheating almost denied them the benefits that they deserved because they passed the test without answering FRQ #6 correctly.

2.   Assume that the students cheated on Free Response Question #6. Describe three reasons why cheating at school is not a good idea and how this relates to the situation of the students in Mr. Escalante's class. Suggested Response: Six reasons are set out in the section on Some Problems With Cheating. The best answers will include at least the first two and one other.

RESPONSIBILITY

(Do what you are supposed to do; Persevere: keep on trying!; Always do your best; Use self-control; Be self-disciplined; Think before you act -- consider the consequences; Be accountable for your choices)


3.   Many teachers and school administrators as well as children and parents have seen this film. Why aren't all children taking the AP Calculus test or engaging in some other specialized effort to excel? What about you? Are you making some special effort in your life to excel? Suggested Response: There is no one correct answer to this question.

4.   Mr. Escalante got angry at Angel and unfairly punished him. The only reason that this did not have disastrous consequences was that Angel was committed and resourceful. How does this incident show the need for self-control by both Angel and Mr. Escalante? Suggested Response: Angel had to control his anger and disappointment with Mr. Escalante. But he was able to step outside of himself, see why Mr. Escalante was angry, see that some of it was justified, and that he could overcome that anger with the abuela stratagem. As for Mr. Escalante, he should have listened to Angel's excuse and if he questioned it, he should have made Angel produce a record from the hospital or a note from his grandmother. However, Mr. Escalante was flexible enough to see that if Angel was willing to resort to the "abuela" stratagem, Angel was interested enough to deserve a third chance.

3. Mr. Escalante begins to pay more attention to his students than to family members and to ignore important health issues, thus placing himself at risk. What does this say about his character and how might these issues work against his AP program in the long run? Suggested Response: Answers will vary. Students may see Mr. Escalante's determination as more than simply wanting to see students succeed; he may be making a political point about the injustice of the poverty and racism in the educational system. It would probably be impossible for most teachers to sustain M. Escalante's level of dedication over time. Despite efforts of his successor, Mr. Escalante's program at Garfield collapsed after he left the school. The achievement gap has broadened in the years since the Garfield experience.

ADDITIONAL ASSIGNMENTS

  • Engage in a mock trial or debate about whether Mr. Escalante's students cheated;
  • Ask students to write an essay answering any one or a group of the questions from the Comprehension Tests or Discussion Question for this movie;
  • Ask students to give a class presentation, alone or in groups, responding to any of the questions from the Comprehension Tests or Discussion Question for this film;
  • Students can be asked to research the history and current status of the Educational Testing Service;
  • Students can be asked to research and discuss patterns of test scores for various standardized tests for different types of communities and answer the question: "What do these patterns tell us about the various communities studied and about the students who attend school in those communities?";
  • Ask students to conduct a simulated mini-lesson preparing the class for an important examination on a specific subject. Require them to use a prepared lesson plan that includes a motivational lecture; and
  • Assignments, Projects and Activities for Use With Any Film that is a Work of Fiction.

  • Escalante: The Best Teacher in America by Jay Mathews, 1988, Henry Holt and Company, New York.






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