Branching Out

A principal asks teachers to work together on an interdisciplinary unit meant to promote critical thinking, self-directed learning, and diversity. Teachers have to integrate their disciplines without sacrificing time needed to master specific content. 'How am I supposed to fit Latin American history into pre-algebra?' The project encourages teachers to branch out and take risks for the sake of student learning.

The principal introduces the idea of creating an interdisciplinary unit.

“And, that’s why I think an interdisciplinary approach would be good for Westwood” Tom Evans said, turning off the overhead.

“Why just us and not the rest of the faculty?” asked Bill Bryant, the Latin American history teacher.

“Well,” the middle school principal explained, “First, I think that the seventh grade is well-suited for interdisciplinary work. Earth science and Latin American studies seem like a natural fit. Also, and don’t let this go to your heads, but the seventh grade has some of our finest teachers. Fred, I’ve seen you be incredibly creative in the projects you use to teach English; Ed, I know that no matter what, your students are going to learn math. Finally, we need a pilot so that we can learn about how interdisciplinary approaches work, and specifically how they can work within our program. Once you all are successful, we’ll have something that we can bring to the rest of the faculty. Something we can build on as a model. I’d like to see you construct portfolios of the students’ work, then we can evaluate them to determine the effectiveness of the project.”

Katy Fuller shifted in her seat. Tom had attended the National Association of Independent Schools (NAIS) conference in New York two weeks ago, and interdisciplinary study was obviously this year’s fad. Katy recalled that Ted Sizer was supposed to give the keynote address at the conference, and Tom must have attended a workshop or two. The portfolio assessment he mentioned was a holdover from his NAIS trip two years ago. Most teachers put together portfolios of student work, but Katy knew—being guilty herself—that the “true” classroom assessment was still the same pencil-and-paper tests they had always used. But she liked the sound of this project. It just might work.

Ted Sizer’s Coalition of Essential Schools

“Now what would the theme of our project be?” asked Katy.

Tom shrugged. “Up to you. I’m not going to tell you what to teach or how to teach it. I just want you to work together so that students can see how topics span the curriculum. We want them to think across subjects, not just within them. I think you all know that the lines drawn between subject areas are rather arbitrary.”

“Now, I’m not sure that I buy that, Tom.” Ed Filcher, the pre-algebra teacher said. “I have a hard enough time covering what I need to prepare these kids for beginning algebra next year. I can’t afford to take a two-week vacation from the text.”

“No one says you need to. Just integrate work from the other subjects areas.”

“I don’t see that as being feasible at all,” said Ed.

“Why not?” asked Katy, irritated. She liked Ed, but sometimes he could be so inflexible. “I use math all the time in science. Why can’t you use science—or social studies, or English, for that matter—to teach math? Why can’t the kids learn that there are math principles present in the world all around them, and not just in a text book?”

“Well, for one thing, because it took me five years to finally find a text that lays out pre-algebra in a way that makes sense to students. If I start bringing in all these extraneous issues, it’s just going to distract the kids from what they really need to know.”

Tom jumped in. “The point is that our students need, and are not getting, development of critical thinking skills that reach beyond the subjective structure of the curriculum. We need an approach that will generate creativity, will help develop new ways of thinking about the curriculum, and encourage self-directed learning. We need kids to work on projects that cultivate their ability to apply skills and content to complex situations, something that multiple-choice testing and a Scantron can’t assess. I’m not saying you’re wrong, Ed. I absolutely agree our students need to learn pre-algebra, or else we’ll hear about it from the high school teachers. I just don’t see why that type of learning has to be exclusive of everything else we do.”

See the philosophy of Westwood Country Day School below:

Katy could see Ed’s jaw set. “Because I don’t have enough time to cover what I need to as it is. I don’t see a problem with learning academics for their own sake. If I start doing projects and talking about tropical jungles, then I’m losing time to cover material that these kids will need next year. ”

Tom replied, “If you don’t want to do this, I won’t force it on you. But think about it for a few days before you make a final decision. I’d like to give this a try and see what we learn. If it doesn’t work, we’ll drop it or fix it. Let’s meet again next week and discuss it more.”

Teachers begin to plan the interdisciplinary unit.

Katy was getting excited about planning for the project. She noticed that Tom and Ed had met privately at least once, and Ed had finally consented to joining the project. They had scheduled it for two weeks in the spring, and were beginning to discuss topics. Sitting in between Bill Bryant, the social studies teacher, and Fred Polk, the English teacher, in the teachers’ lounge, Katy addressed Bill.

“You know, I always felt that we should somehow tie your course in with mine. We cover a lot of information on climates, mineral deposits, and even eco-cycles. We should show the students that there are natural connections between what we cover in earth science and the economies and societies of any country.”

“Absolutely.” Bill smiled. “When do you teach about climates and minerals?”

“Well, actually, we’re just getting into minerals right now,” said Katy. “I like to do the climate section in early spring—a lot of the students travel with their families to different climate zones during their spring break, and it helps to generate discussion about weather patterns.”

“OK, let’s plan something around climates and natural resources—maybe lumber and forestry. There are several sections of our text that get into issues like the balance between industry and environmental concerns like tropical rain forests,” said Bill.

Fred joined in: “You know, it’s always bothered me how students don’t relate what they learn in one subject to what they learned in another. It’s as if they don’t give a subject a second thought once they leave the class. In the spring, I teach how to write business letters, and the students could write embassies or other organizations to collect information. I could also find some literature that might reflect a South American theme. Theroux’s Mosquito Coast would pick up your themes of industry clashing with nature.”

“How about using the theme ‘vanishing rain forests’ for the project? There’s been plenty on that in the news, and the students tend to feel pretty strongly about environmental issues,” said Bill.

“How about just deforestation in general?” responded Katy. “That way, I could look at the problem not only in South America, but in the U.S. as well. We could look at some of the conflicts about timberlands out west. The spotted owl and all that.”

Fred leaned forward in his chair. “You better watch out, Katy. Tommy Billings’s dad used to be a state senator and made most of his money from timberland.”

“Oh, come on, Fred,” said Bill. “It’s been years since he’s been in office. It just makes me sick the way our development office and the administration fawn all over him and treat that has-been like he was some VIP.”

“I see I touched a nerve here,” replied Fred. “I’ll remind you that he’s “only a political has-been” when he barges into Tom’s office complaining about the left-wing environmental psychos on the faculty.”

Just then, Ed Filcher walked in, some thirty minutes late for the meeting.

“Heavy traffic, Ed?” asked Bill, with just a hint of sarcasm.

“Sorry, I had something personal and unexpected come up this morning.”

Bill, Fred, and Katy caught him up on the discussion. “I still don’t see how I’m supposed to work rain forests into pre-algebra,” said Ed, with some exasperation.

Katy turned toward him. “Oh come on. What if I get the students to do a field project in my class? You can use the data they collect to teach your lessons. I’m flexible, and I’m sure we can come up with something that won’t disrupt your plans.”

“OK. OK. Get me a list of the data types you’ll be working with, and I’ll see if I can work it in somehow. If there’s just not a fit I’ll let you know. But listen Katy, I absolutely refuse to sacrifice academic rigor for the sake of this project.”

Bill got up and walked toward the coffee machine as he said, “Ed, Ed, Ed… We all feel that way, but what we’re talking about is getting the students to think in new ways. Maybe we’ll all learn something by trying a new approach.”

Katy Fuller reflects.

Katy was glad the project was going so well. The teachers had incorporated material from all four classes into the project. In Latin American history, the students were collecting information on deforestation in South American countries. All the teachers agreed it was important to tie South American issues to the United States. In the weeks leading up to the official start of the project, Fred Polk had the students write business letters to embassies, American environmental groups, and government agencies to collect additional information on deforestation rates and practices in both countries. Many students had already received packets of information in response. Teachers hoped they would use the information to make connections to similar issues in the United States.

The students in Katy’s science class were going to use sampling techniques to determine the number of mature trees that grew in an acre of forest in a temperate climate. She had carefully constructed a lesson plan that meshed with the topics in the other courses.

See Katy’s lesson plan below:

Four teams of four or five students each would mark off twenty-yard square plots in the woods.

Each tree in the plot would be identified by species and stage of growth. Ed Filcher, who had agreed to work the data into his unit on percentages and ratios, would have the students calculate an estimate for the volume of wood in an acre of forest, and eventually determine the dollar value of an acre of wood. They could then calculate the value of the timber on the Westwood property.

Katy hoped that by actually counting trees and associating a dollar amount with the timber, the students would begin to appreciate forests as valuable national resources. They might also be able to apply these lessons to their study of other countries and to consider environmental issues here in the United States. Later they would discuss the principles of conservation. They would consider which harvesting techniques help preserve trees and how such techniques might vary by climate and by type of forest. Katy felt a little uneasy about tackling issues that moved toward biology. She reasoned, however, that the process was in keeping with the interdisciplinary spirit of the project.

Students work on a field project to estimate the value of timber.

The Westwood campus had several acres of wooded land on its southern end, and the class was standing in the middle of it. Each student team was responsible for developing a procedure for marking off a sample plot. Katy looked at the faces of the students in front of her. She knew this particular team tended to rush through assignments and had not done a very good job of thinking through tasks. She had decided to let problems emerge while students were out in the field to help reinforce the value of good planning.

“How are you going to make sure the lines are square?” Katy asked the group of students as they ran an orange line around one tree.

“We should get one of those square things to make sure the angle is 90 degrees,” said Felix. Felix’s father was an aeronautical engineer, and Felix also hoped to design airplanes some day. This was probably the weakest of the four groups, but she hoped Felix’s enthusiasm would help his colleagues keep going in the right direction—if only Felix didn’t get distracted.

Katy responded, “Good idea, but you don’t have one of those square things, and I’m not going to let you walk back to the building. What else can you try?”

“Why not just do it and see how it turns out? I mean if it doesn’t look right, we’ll move the lines around,” said Tyler.

Katy took a deep breath. Tyler always seemed to find a way of making an activity seem like a total waste of time. “Well, Tyler, trial and error is certainly one method. But as scientists, we’d like to find a way to be a bit more precise.”

Tyler seemed dissatisfied with that remark, and countered, “Well, I’m not a scientist. Face it, if we’re off a little here or there it really isn’t going to make any difference. What’ll happen, we might miss a tree or something?”

Katy was amazed at the disrespectful manner that many of the students in the school used with adults. Katy wasn’t sure whether the flippant attitude was driven by social class or was just part of the culture of young people today. She liked to think that kids were kids, no matter what their backgrounds, but she also knew these students came from a culture very different from her own.

Katy could tell that Anne wanted to say something but was obviously intimidated. “Anne, what do you think? Do you have a suggestion for the group?” she asked. Anne turned her eyes downward and remained silent. Katy decided to wait a few moments to see if a little silence might coax a response from Anne, but then Felix spoke up.

See an analysis of gender dynamics in the classroom below:

“How ’bout the hypotenuse? That would tell us how far the ends should be apart.” Katy was annoyed at Felix for stepping in, but his was an excellent answer. Felix was a careless, sloppy thinker, but he had flashes of brilliance.

“That’s a great way of doing it,” said Katy. “What equation would you use?”

No one responded.

Katy glanced around the group. “Does this ring any bells? ‘The square of the hypotenuse equals the sum of the square of the sides.’ ”

“Oh yeah. Now I remember,” said Felix.

“But, do you want the square of the hypotenuse?” continued Katy.

This time Reza, the fourth member of the group, jumped in. “Yes we do. ‘Cause once you have that, you just root it and you get the hypotenuse.” Katy was glad that Reza had spoken up, although she suspected he was driven more by showing up a Jewish classmate than by searching for academic truth. The Islamic students tended to be very cliquish, and their parents were a small but vocal constituency. Reza’s family was Islamic and had left Iran at the same time the Shah was overthrown. Westwood was one-third Jewish, and out of practical necessity, the school closed on Jewish holidays. This added to the tension between the Jewish students and the handful of Islamic students attending the school. The Islamic students believed their holidays were not valued as much as Jewish and Christian holidays. Tom Evans had tried to acknowledge Islamic holidays at middle school assemblies by explaining why some children would be absent on certain days. The Islamic students seemed irritated by what they perceived as token recognition; the other children just seemed bored.

Katy heard some yelling and glanced off toward the other groups who were obscured by the trees.

“Very good, Reza. Now we just take the square root of both sides. So you end up with …” Katy scratched some figures on the pad.

“Now, when you find ‘c,’ the hypotenuse, how will that help you? Anyone besides Felix know?”

Reza answered, “That’s how far apart the corners will be.”

“What corners?” asked Katy.

“The corners. The ones facing each other,” responded Reza.

“You mean diagonally?” queried Katy.

Gesturing, Reza replied, “Right. Across from each other.”

“Correct.” So if your corners are ‘c’ distance apart, you know they are the right distance, and you know you have a square. Take a few minutes to figure out the numbers you want to use. Once the Quality Control person—isn’t that you Tyler?—checks the work, you all can measure the line and assign the jobs for walking it out. I’m going to check on the other groups, but I’ll be back in a few minutes.”

Katy walked toward the next group, scanning the woods around her to try and see how the others were doing. She heard laughter from the farthest group, prompting her to check on them first; she could work her way back to the closer groups.

“Well, you haven’t gotten very far,” said Katy. Fred and Stan were just tying off the first side of the plot.

“It’s been taking longer than we thought,” called Fred, which caused Stan to laugh for some reason. Stan was one of a number of African-American scholarship athletes who traveled an hour on public transportation each day to come to Westwood from the inner city. His goal was to get a football scholarship at the state university. Katy thought he had a good shot at it. He was bright and unusually mature for his age, perhaps the result of a less-than-easy life. The students looked up to Stan. Because of his athletic ability and inner-city worldliness, Stan had become a hero of sorts to many of his classmates. Katy knew that Stan exerted a positive influence on the other students. She just hoped the Westwood environment was serving him as well.

“You all had better pick up the pace. You’re falling behind the others,” said Katy.

“Mrs. Fuller?” asked Sara, who was writing something on a pad.

“Yes?” answered Katy. Sara was a pretty, very likable girl who worked hard most of the time.

Katy noticed that Fred and Stan both looked up as Sarah spoke. “Aren’t a lot of trees lost to forest fires?”

“Yes, they are. That is a good point: not all deforestation is intentional. Remember to bring that up tomorrow in class,” replied Katy.

Katy knew this group would get the work finished, but they needed some supervision to encourage efficient use of time. She made a point of walking past Fred and Stan just to project her presence. As she passed near Fred, she thought she smelled the lingering scent of smoke from his clothing. At first, she thought the worst—pot. But then she got a second whiff and decided it was from cigarettes.

She was caught in a moment of indecision. Her first instinct was to call him on his behavior. If he had smoked out here in the woods, he couldn’t have had time for more than a puff or two in the time he was out of her sight. He might have tried it just for the thrill of being bad or to impress his peers. More likely, he probably had a cigarette in the boys’ restroom before class—a growing problem that Mr. Evans had recently addressed at the middle-school assembly. To make matters worse, Mr. Evans was not a fan of outdoor classes, and all she needed was an incident like this to put her on the defensive every time she decided to take her class outside. Forget it. She had smoked a few cigarettes at school in her own time. She’d let this one slide.

Ed Filcher prepares his math class to use the science data.

Ed wiped the chalk dust off his hands. “Any questions?” The room was silent. “OK, now you try problem three. When you’re done, I’ll ask for a volunteer to work it on the board.”

Ed was a retired army officer who had started teaching at Westwood to supplement his pension and to continue being productive. The public schools would only hire him as a substitute teacher, a prospect which held little appeal for him. So, he had applied to Westwood which, because it was private, was not bound by state certification requirements.

Ed believed in discipline and hard work. He also thought these concepts were foreign to many of today’s youth and their parents. Young people needed and craved something firm to hold on to. Sure, some of them tested your resolve; but what they were really testing was how much you cared about them. Did you care enough to stick to your principles? Or did you take the easy way and cave in, or pass the problem along to someone else? He thought too many parents took the easy way out, because they did not have the time or patience to do otherwise. Maybe some of them felt guilty about disciplining their children in what little “quality” time they actually spent together as families.

He looked out over the students, heads down, scribbling away at the problem. Ed had few discipline problems, because students knew he cared enough to sit down with them and work out any problems eye-to-eye. He couldn’t remember the last time he sent someone to the office. The students understood that if they needed help with math, he would come in early or stay late regularly to give that help. They also knew they would see him in the stands at most of their sporting events and school plays.

He really didn’t mind the deforestation project. He had only resisted because he believed his classroom worked well, and this was an unsolicited disruption. The science teacher wanted him to introduce some geometry so students could estimate the height of trees. It wasn’t a bad idea, but he thought that introducing some concepts too early would be confusing, especially to the weaker students. He had agreed to teach a volume formula early, so students could estimate the volume of wood in a tree. The students weren’t ready, however, for estimating the height of trees geometrically, no matter what Katy Fuller said. They would have to settle for using values from the Peterson’s Field Guide to North American Trees to get the average heights of the different species.

“OK, everyone, let’s get going. Jessica, you’re our volunteer this time,” Ed boomed. The class laughed because no hand had been raised.

Jessica went to the board and started working the problem, which was a proportion word problem. When she finished, she stepped back from the board.

“Does anyone disagree with Jessica’s answer?” Several hands shot up.


“The 28 should be on the bottom, and the 16 should be on the top.”

“Why is that?” asked Filcher.

“Because trees are on the bottom on the left side, so trees should be on the bottom on the right side.”

“Very good. Do you see that, Jess?” Jessica blushed and nodded. She stepped up to the board and corrected the problem.

“Now, in the next question you need to find the hypotenuse of the triangle before you can use a ratio to solve the rest of the problem. You remember the Pythagorean theorem from last year: the square of plus the square of b equals the square of c. So you square both sides of the triangle and ….. Yes, Reza?”

“Mrs. Fuller told us the hypotenuse was equal to the square root of the square of a plus the square of b. Besides, Mrs. Fuller says its dumb to memorize formulas when you can just look them up in a book. She always gives us all the formulas on her tests.”

Ed’s face flushed. He didn’t know if he was more angry at Reza for trying to show off in class, or at Katy Fuller for taking it upon herself to teach his subject. This was what he feared. The students would get conflicting information from different teachers. Was it now his responsibility to teach Katy how to teach math? Confusion between the teachers over such basic concepts would lead to confusion among the students.

“Well, Reza, you and Mrs. Fuller are technically right. What you’ve done is to turn the equation around. We’ll be doing the same steps, but in a different order, and our equation will be written differently. We’ll start with the equation as Pythagoras wrote it, which is how you learned it.”

He could see the confused looks on some students’ faces. Ed wanted them to learn and understand the concept first, then they could work on the sequence of variables and the equivalency of equations. “We’ll use this equation—the same one you used last year—to make sure everyone understands what we are doing.” He was going to give Katy an earful on this one.

As class drew to a close, Ed said, “That’s it for today. Tomorrow we’ll start working with the data you’re collecting in Mrs. Fuller’s class, using the same tools we learned last night and today. I also want you to read section 10 on calculating the volume of a cylinder. We’ll use that equation tomorrow when we look at the volume of wood in a tree. Now, Reza, you be sure to tell us if you’ve learned a way to calculate volume that’s different from the formula in the book.”