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Mathematics Goes to the Movies

by Burkard Polster and Marty Ross


Stand and Deliver (1988)

Stand and Deliver is the story of Jaime Escalante (played by Edward James Olmos), a mathematics teacher from Bolivia who comes to Garfield High, a poor and poorly run school in the Latino area of East Los Angeles. He is a humorous, charismatic and demanding teacher, who persuades his class to take the Advanced Placement exam in calculus. The class performs so well that they are accused of cheating by the testing authorities.

Here is the chapter from our book dedicated to this fabulous movie.

And here is a transcript of the relevant dialogue

Escalante enters his first classroom, to be confronted with the chaos of noisy, uncaring students cracking jokes, throwing paper balls, and so on.
ESCALANTE: This is Math 1-A
UNSEEN STUDENT: I don’t need no math. I got a solar calculator with my dozen doughnuts.
LUPE (Ingrid Oliu): The bus is exact change. No big deal.
The bell rings, ending the class.

Escalante is at the front of the class, dressed in a butcher’s apron and hat, holding a meat cleaver. He swings down the cleaver, chopping an apple in half. He points at Claudia (Karla Montana), who has a quarter of an apple on her desk.
ESCALANTE: Whatchyou got?
CLAUDIA: It’s an apple.
The class laughs.
ESCALANTE: How much?
CLAUDIA: What do you mean?
ESCALANTE points at Lupe, who has half an apple on her desk.
ESCALANTE: Whatchyou got?
LUPE (shrugs): Half.
ESCALANTE (in comic accent): Goood! Escalante motions to Ana (Vanessa Marquez) who has three quarters of an apple on her desk. What you got?
ANA (whispering): Missing 25 per cent?
Escalante waddles up to her, and leans over.
ESCALANTE (whispers): What?
ANA: It’s missing 25 per cent.
Escalante picks up and examines the apple.
ESCALANTE (in a singing voice): That’s right. Missing 25 per cent. Escalante leans intimately towards Ana. Is it true that intelligent people make better lovers? He walks to the front of the room, and points to Pancho (Will Gotay) who has eaten his apple. Hey, what you got?
PANCHO: I gotta core. Class laughs.
ESCALANTE: You owe me a hundred per cent. And I’ll see you in the People’s Court. Class laughs. Everyone please open your book, chapter 2, page 26, multiplication of fractions… and percentages. He points at the various apple portions around the room. 25 per cent, 50 per cent, 75 per cent… Two cholos, Chuco (Daniel Villarreal) and Angel (Lou Diamond Phillips), have just arrived and sullenly walk up to Escalante … and a hundred per cent.
Escalante takes their late slips, and sits Chuco in the front of the class. After setting the class to work, he whispers to Chuco.
ESCALANTE: You got to come to this class prepared.
CHUCO: I do the work in my head.
ESCALANTE: Ohhh! You know the times tables?
CHUCO: (sticking up his thumb) I know the ones, (sticking up his second finger) the twos, (sticking up his middle finger, in an obscene gesture) the threes…

ESCALANTE: Finger man. I heard about you. Are you the finger man? I’m the finger man too. You know what I can do? He holds his ten fingers splayed. I know how to multiply by 9. 9 times 3. 1, 2, 3 (counting off with his fingers, to leave two fingers on one side his crooked finger, and seven on the other side). Whaddyou got? (wiggling his fingers) 27!
6 times 9. 1, 2, 3, 4, 5, 6. Whaddyou got? (wiggling his fingers) 54! Yeah. Want a hard one? How about 8 times 9? 1, 2, 3, 4, 5, 6, 7, 8. Whaddyou got? (wiggling his fingers) 72!
DISCUSSION: Escalante has shown a nice trick for multiplication by 9; the key to the trick is that the sum of the digits is always divisible by 9.

ESCALANTE: This is basic math, but basic math is too easy for you burros. So I’m gonna teach you algebra because I’m the champ. And if the only thing you know how to do is add and subtract, you’ll only be prepared to do one thing – pump gas. …. Who ever heard of negative and positive numbers? Anybody.
PANCHO: Yeah. Negative numbers are like unemployment….
Escalante walks around the class.
ESCALANTE: You ever been to the beach? You ever play with the sand?
He points towards threatener. Finger man. You ever dig a hole? The sand that comes out of the hole, that’s a positive. The hole is a negative. (To the class) That’s it. Simple. Anybody can do it. Minus two plus two… equals He looks towards Angel. Net-head! Oralé. Answer it. Lou shuffles and doesn’t respond. Come on, you know the answer. Escalante walks up to him. Minus two plus. Fill the hole…. Oralé. Come on, a negative two plus two equals. Anybody can do it. Fill the hole. He starts whispering. Minus two plus two equals. Come on, just fill the hole. You can do it. You going to let these burros laugh at you? Minus two plus two equals. I’ll break your neck like a toothpick, click! Oralé.
ANGEL (sullenly): Zero.
ESCALANTE: Zero. You’re right. Simple. To the class. That’s it! Minus two plus two equals zero. He just filled the hole. Did you know that neither the Greeks nor the Romans were capable of using the concept of zero? It was your ancestors, the Mayas, who first contemplated the zero, the absence of value. True story. You burros have math in your blood… He draws parentheses on the blackboard. Oralé! O.K! Parentheses… means multiply. Every time you see this, you multiply. A negative times a negative equals a positive. A negative times a negative equals a positive. Say it! A negative times a negative equals a positive. Say it!
CLASS AND ESCALANTE: A negative times a negative equals a positive.
CLASS AND ESCALANTE: A negative times a negative equals a positive. A negative times a negative equals a positive.
ESCALANTE: I can’t hear you!
CLASS AND ESCALANTE: A negative times a negative equals a positive.
CLASS AND ESCALANTE: A negative times a negative equals a positive.
CLASS AND ESCALANTE: A negative times a negative equals a positive.
ESCALANTE (softly): Why?
DISCUSSION: It is certainly true that zero and negative numbers were concepts unknown to the Greeks and the Romans, and that the Mayans did have zero as part of their number system, at least from around 665 AD. However, the Mayan use of zero seems to be only as a placeholder in positional notation, rather than seeing 0 as a number in its own right. By contrast, and around the same time, the Indian mathematician Brahmagupta was considering (not too successfully) the arithmetic of 0, treating 0 as a fully-fledged number.

The faculty are discussing the danger of the school being put on probation.
PRINCIPLE MOLINA (Carmen Argenziano): Now, if we fail, we’ll lose our accreditation.
RAQUEL ORTEGA, HEAD OF MATH (Virgina Paris): We fail! You can’t teach logarithms to illiterates. Look, these kids come to us with barely a seventh grade education. There isn’t a teacher in this room who isn’t doing everything they possibly can.
ESCALANTE: I’m not. I could teach more.
ORTEGA: … I’m sure of Mr. Escalante’s good intentions. But he’s only been here a few months.
ESCALANTE: Students will rise to the level of expectations, Señor Molina.
MOLINA: What do you need, Mr. Escalante?
ESCALANTE: Ganas. That’s all we need is ganas.

Escalante is handing out a quiz.
ESCALANTE: You already have two strikes against you. There are some people in this world who will assume that you know less than you do, because of your name and your complexion. But math is the great equalizer… You’re gonna work harder than you ever worked before. And the only think I ask from you is ganas. Desire.

The formula for the difference of two squares is on the blackboard in the background.

The difference of two squares.

We see a text, “Algebra Two”, on Ana’s desk.
ESCALANTE: Factoring O.K. Green light, red light. Anybody. Ana.
“Green light – red light” was Escalante’s expression for distinguishing between easy factorisation, and factorisation which needed more thought.

Escalante is teaching algebra. On the blackboard are workings for the facorization of polynomials.
ESCALANTE: Everybody look at the board. Will someone please read for me what’s on the board? Anybody.
CLASS: Juan has five times as many girlfriends as Pedro. Carlos has one girlfriend less than Pedro. The total number of girlfriends between them is twenty. How many does each gigolo have? Molina and Ortega walk into the room, are teased by the students.
ESCALANTE: OK, OK, OK. How many girlfriends does each gigolo have? Anybody. Tito raises his hand. Think you got it, Einstein? You think you gonna do it?
TITO: Juan is X. Carlos is Y. Pedro is X plus Y. Is Pedro bisexual or what?
ESCALANTE: I have a terrible feeling about you. Tito blows Escalante a kiss.
CLAUDIA: Kemo. 5X equals Juan’s girlfriends?
ESCALANTE: You’re good now, but you’re gonna end up barefoot, pregnant, and in the kitcheeen. Laughter from the class.
RAFAELA (Lydia Nicole): Can you get negative girlfriends?
ESCALANTE: No, just negative boyfriends. Please forgive them, for they know not what they dooo!
ANGEL: Carlos has X-5 girlfriends, que no?
ESCALANTE: Que no? is right. Que no. Lupe raises her hand. The answer to my prayers!
LUPE: May I go to the restroom please? Laughter.
ESCALANTE: In ten minutes. Hold it. He walks up to Javier (Patrick Baca). Señor Maya. Hit it. Javier smugly wiggles his pencil.
JAVIER: It’s a trick problem, Mr. Kemo. You can’t solve it unless you know how many girlfriends they have in common. Right?
ESCALANTE (to Molina and Ortega): It’s not that they’re stupid. Itt’s just that they don’t know anything.
JAVIER: I’m wrong? Ana has just come to the door.
ANA: X equals Pedro’s girlfriends, 5X equals Juan’s girlfriends, X-1 equals Carlos’s girlfriends. X plus 5X plus X-1 equals 20, so X=3. The class claps. Ana sits down.
PANCHO: Kemo, this stuff don’t make no sense unless you show us how it works in the real world.
ESCALANTE (to Molina and Ortega): Do you think it would be possible to get a couple of gigolos for a practical demonstration? No, no, no. No, no. Just kidding.
DISCUSSION: Ana’s is the natural approach. The suggestions of Tito and Angel make no sense.

The class is on a field trip to a technical company. Joe (Tyde Kireney) and Escalante are staring at computer screens. Pancho leans over their shoulders.
PANCHO: What kind of math is this?
JOE: This particular one that’s up right now is calculus.
ESCALANTE (to Pancho): You’ll get it in college.
JOE: Well, my daughter uses this program in her high school.

Escalante is in the staff room with the other teachers.
ESCALANTE: I wanna teach calculcus next year.
MOLINA (laughing): Boy. That’s a jump.
ORTEGA: That’s ridiculous. They haven’t had trig, or math analysis.
ESCALANTE: They can take them both during the summer.
ORTEGA: You expect our best students to go to summer school.
ESCALANTE: From 7 to 12, everyday including Saturdays. Yep, that’ll do it.
MOLINA: Our summer classrooms are reserved for remedial courses.
ESCALANTE: If you wan to turn the school around you’re gonna have to start from the top.
ORTEGA: Mr. Escalante, don’t lecture us. Our kids can’t handle calculus. We don’t even have the books.
ESCALANTE: If they pass the advanced placement test, they get college credit.
ORTEGA: There are some teachers in this room who’d have trouble passing the advanced placement test.

The class is studying trigonometry over the summer.

The class is starting the new year. Escalante discusses the AP calculus class with them.
ESCALANTE: We will go step by step, inch by inch. Calculus was not made to be easy. It already is.
The class leaves, and Angel walks in.
ANGEL: Hey, Kemo. Prouda me? I’m the first one here! He Sees “CALCULUS” written on the blackboard. What’s cal-coo-lus?

Claudia is persuading her mother (Yvette Cruise) to permit her to take extra classes.
CLAUDIA: Mom, calculus is math that Sir Isaac Newton invented so he could figure out planet orbits, but he never bothered to tell anybody about his discovery until this other scientist guy went around claiming he had invented calculus. But the guy was so stupid that he got it all wrong, and so Newton had to go public and correct his mistakes. Don’t you think that’s neat?
CLAUDIA’S MOM: For a genius, Newton was an idiot.
DISCUSSION: Claudia is, of course, referring to Leibniz, the other inventor of calculus. Claudia’s version of the history is correct except for the implicit suggestion that Leibniz may not have come up with the ideas independently, and the explicit suggestion that Leibniz was stupid and got it all wrong.

The students have come early to class. Escalante is teaching the method of obtaining volumes of revolution by disks.
ESCALANTE: One, you got the graph, right here. Two, the strip, the most important part is right here. It’s the radius of rotation. That’s it. Anybody got any questions?
Escalante sees Angel pointing to Tito, asleep. Behind Angel is a poster on the wall about the real numbers:
1. X>0 ? X<0 AND ZERO
Escalante walks towards Tito. Anybody can do it, as long as you remember one basic element, and that is the element of surprise. He starts slapping Tito gently with a towel. Stay awake as you’re waking up. Wake up this morning! How are you? Bring toothpicks to pinch open your eyes. You understand what I mean, Johnny?
TITO (groggily): I was swimming with dolphins whispering imaginary numbers, looking for the fourth dimension. Escalante puts the towel on Tito’s forearm, and pushes Tito’s head onto it.
ESCALANTE: Good! Go back to sleep. That’s very good.

The calculation of the two-sided limit of a non-differentiable function is on the blackboard in the background.

Pancho is working an integration by parts problem on the blackboard. He looks back, questioningly, to Escalante, who grunts disapproval.
ESCANALANTE: Try the shortcut. This is easy. Baby stuff for boyscouts.
PANCHO: Kemo, my mind don’t work this way!
ESCALANTE: Tic-tac-toe! It’s a piece of cake upside down. Watch for the green light. Pancho stares at the board, and then thumps it with his fist.
PANCHO: I’ve been with you guys two years! Everybody knows I’m the dumbest. I can’t handle calculus! These guys have a better chance of making the A.P. test without me. Javier snickers.
PANCHO: Don’t laugh.
ESCALANTE: How could we laugh? You’re breaking our hearts.
PANCHO: Don’t do this, Kemo.
ESCALANTE: How noble. To sacrifice himself for the benefit of the team! He approaches Pancho at the board. Do you have the ganas? Do you have the desire?
PANCHO: Yes! I have the ganas!
ESCALANTE: You want me to do it for you!
ESCALANTE: You’re supposed to say “no”! To the class. Well, I’m going to haveto get tough. Bullets are gonna have to start playing. We’re gonna have to work right through Christmas break. O.K.? As Escalante writes the solution on the blackboard Angel enters at the back of the room. (Behind Escalante, above the blackboard, we see the definition of the continuity of a function, and trigonometric acronym, SOHCAHTOA).

Escalante orders him to leave, and Angel storms out. He continues with the integration problem and talks to Pancho as he writes. Mind you, I think that guy’s got a bigger problem than you. Tic…tac…toe. Simple.

DISCUSSION: Pancho’s calculations are correct but unhelpful, since he has made the wrong choices of u and dv. Escalante’s shortcut method is correct, but doesn’t really address Pancho’s misunderstanding.

Escalante is pointing to the graph of the function , appearing on the overhead projector.
ESCALANTE: This is what’s given. We’re looking for the area in the first quadrant bounded by the curve. What are the limits? Anybody.
TITO: 0 to π/2, sir.
ESCALANTE: Wrong. Lupe.
LUPE: 0 to π/2?
ESCALANTE: What’s wrong with you? This is review.
LUPE: Kemo, I checked my work twice.
ESCALANTE: I’m giving you the graph. Check it again.
ANGEL: No, Kemo, I’m getting the same answer as the gordita.
LUPE: Don’t call gordita, pendejo.
ANA: It’s 0 to π/2, sir.
JAVIER: Yeah. I got the same thing.
ESCALANTE: You should know this. Now, no way. You should know this. What’s wrong with you? This is review! You’re acting like a blind man in a dark room looking for a black cat that isn’t there. What’s wrong with you guys? I don’t believe it. You’re giving me a shot from the back! No way! No way! Escalante storms out of the room.
PANCHO: Kemo finally blew a head gasket.
DISCUSSION: The students are, of course, correct. The scene is used as an indication of the stress upon or the poor health of Escalante. Escalante’s description of the students is actually a famous quotation by Charles Darwin, describing all mathematicians and the very nature of their pursuit; as such, Escalante’s use of it as a description of students (supposedly) making simple mistakes is in a completely different context.

After Escalante has had a heart attack, the class is trying to work on its own. A problem on the quotient rule for differentiation is seen in the background.

The class is passing around solutions from Escalante, written from the hospital.

Escalante returns to the class, greeting the students. In the background is a poster on complex conjugates in the solutions of quadratic equations.
He stands the students against the wall, ready to be asked questions.
ESCALANTE: All right! You got it! Now open your eyes. He addresses Lupe, who is at the top of the line. Y…equal… to LN… quantity X minus 1. What’s the domain?
LUPE: X is greater than minus 1.
ESCALANTE: Noooh! To the end of the line! I been gone two days and you forget already! He addresses Pancho, next in line. What’s the domain?
PANCHO: All real numbers great than 1, X is greater than 1. Escalante smiles and shakes his hand.
ESCALANTE: I told you you could do it. O.K. Kawasaki!

Angel and Chuco are in a car. Chuco looks at the night sky.
CHUCO: Lots of stars up there, Homey. Not too polluted.
ANGEL: The stars aren’t really there, ese. No, what you’re looking at is where they used to be, man. It takes the light a thousand years to reach the Earth. You know, for all we know, they burned out a long time ago, man. God pulled the plug on us. He didn’t tell nobody.
CHUCO: The stars are out there, homeboy. I don’t care what you say.

The students are retaking the AP test after having been accused of cheating. We are looking over the shoulders of students, at their calculations. Ana’s calculations: she is correctly determining that (E) is the correct answer.

Tito’s calculations.

Claudia’s calculations.

The graphs for two of the test problems.

The story is substantially true. Escalante was in real life a brilliant, famous and outspoken teacher (he has now retired to Bolivia). The major fictional aspect of the movie was to compress many years of work, with many classes of students, into two years with one class. Though this is dramatically powerful, it is also importantly misleading in overstating how quickly Escalante could turn around the mathematics program at Garfield, and how quickly he could take a student from mathematical ignorance to formal success.
The story is not so much about the teaching and learning of mathematics. Rather, the story is about Escalante’s power, through teaching mathematics, to make his students understand their own abilities and possibilities. The goal is not primarily to have the students understand and appreciate the mathematics; the goal is to pass the exam, which is the meaningful achievement for the students. In essence this is a part of the story underemphasised in the movie. The quick-trick approach Escalante instilled would also tend to lead to the students making similar and peculiar mistakes, which is what triggered suspicion at the testing service.